Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
Answers
Answer:
1- 35/37
2- 12/37
3- 35/37
4- 12/37
Step-by-step explanation:
The sine of an angle is the ratio of the opposite to the hypotenuse while the cos of an angle refers to the ratio of the adjacent to the hypotenuse. Therefore, the following is true:
Sin D = opposite/hypotenuse = 35/37 -has no simplest form Sin E = opposite/hypotenuse = 12/37 -has no simplest form Cos D = adjacent/hypotenuse = 12/37 -has no simplest form Cos E = adjacent/hypotenuse = 35/37 -has no simplest form
These are fractions that can't be simplified, so they remain the same.
Hope this helps!!
The measure of the trigonometric relations are solved
sin D = 35/37
sin E = 12/37
cos D = 12/37
cos E = 35/37
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔDEF
Now , the measure of sides of triangle are
The measure of side DE = 37
The measure of side EF = 35
The measure of side DF = 12
Now , from the trigonometric relations
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
On simplifying , we get
sin D = 35/37
sin E = 12/37
cos D = 12/37
cos E = 35/37
Hence , the measures of trigonometric relations are solved
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Related Questions
Help..rq................
Answers
Answer: -1/5
Step-by-step explanation:
Answer:
The second one -1/5.
Step-by-step explanation:
1-2=-1 for y and 10-5=5 for x -1/5.
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=70°, and EF = 4.4 feet. Find the length of FD to the nearest tenth of a foot.
Answers
Answer:
FD= 1.6 ftStep-by-step explanation:
Seems like an easy trig question so let's get to it.
1) Draw the right triangle to make it easier to solve (right triangle because we have a 90 degree angle)
2) Find the last angle measure by adding 90+70= 160 and 180-160= 20 so the last angle measure is 20.
3) Use trig function, tan20= x/4.4 to find the answer of x (FD) to be 1.6. Therefore, the FD value will be 1.6 ft.
Use the distance formula to find the distance between each pair of points round to the nearest 10th if necessary
Answers
Given:
The pairs of points are:
a. A(-6,-4), B(-3,-1)
b. C(3.5,1), D(-4,2.5)
c. X(5,-5), Y(-5,5)
To find:
The distance between the pair of points by using the distance formula.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
a.
Using the distance formula, the distance between the points A(-6,-4) and B(-3,-1) is:
[tex]AB=\sqrt{(-3-(-6))^2+((-1-(-4))^2}[/tex]
[tex]AB=\sqrt{(3)^2+(3)^2}[/tex]
[tex]AB=\sqrt{2(3)^2}[/tex]
[tex]AB=3\sqrt{2}[/tex]
[tex]AB\approx 4.2[/tex]
Therefore, the distance between the points A(-6,-4) and B(-3,-1) is about 4.2 units.
b.
Using the distance formula, the distance between the points C(3.5,1) and D(-4,2.5) is:
[tex]CD=\sqrt{(-4-3.5)^2+(2.5-1)^2}[/tex]
[tex]CD=\sqrt{(-7.5)^2+(1.5)^2}[/tex]
[tex]CD=\sqrt{56.25+2.25 }[/tex]
[tex]CD=\sqrt{58.5 }[/tex]
[tex]CD\approx 7.6[/tex]
Therefore, the distance between the points C(3.5,1) and D(-4,2.5) is about 7.6 units.
c.
Using the distance formula, the distance between the points X(5,-5) and Y(-5,5) is:
[tex]XY=\sqrt{(-5-5)^2+(5-(-5))^2}[/tex]
[tex]XY=\sqrt{(-10)^2+(10)^2}[/tex]
[tex]XY=\sqrt{100+100}[/tex]
[tex]XY=\sqrt{200}[/tex]
[tex]XY\approx 14.1[/tex]
Therefore, the distance between the points X(5,-5) and Y(-5,5) is about 14.1 units.
If the probability that the Islanders will beat the Rangers in a game is 78%, what is
the probability that the Islanders will win at least five out of six games in a series
against the Rangers? Round your answer to the nearest thousandth.
Answer:
Submit Answer
Answers
Answer:
(17/25)^5 = 0.145393 = 14.539%
Step-by-step explanation:
78% = 78/100 or 17/25 simplified
probability of winning each game is 17/25
The probability that the Islanders will win at least five out of six games in a series against the Rangers is 0.4.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
The probability that the Islanders will win the Rangers in a game = 78% ⇒ [tex]0.78[/tex]
The probability that the Islanders will lost the Rangers in a game is
⇒ [tex]1-0.78=0.22[/tex]
The probability that the Islanders will win at least five out of six games in a series against the Rangers is
⇒ [tex]6C_{5} (0.78)^{5}(0.22)^{1}[/tex]
⇒ [tex](6)(0.2887)(0.22)[/tex] [∵ [tex]6C_{5} =6[/tex]]
⇒ [tex]0.3811[/tex] ≈ [tex]0.4000[/tex]
Hence we can conclude that the probability that the Islanders will win at least five out of six games in a series against the Rangers is 0.4.
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There is a total of 45 playoff games over c days. Write the expression of the number of playoff games happening each day.
Answers
Answer:
[tex]\frac{45}{c}[/tex]
Step-by-step explanation:
Playoff games played = 45
Number of days taken for the playoff games = c days
Number of playoff games played in one day = [tex]\frac{\text{Number of games played}}{\text{Total number of days}}[/tex]
= [tex]\frac{45}{c}[/tex]
Therefore, expression for the number of playoff games played in a day = [tex]\frac{45}{c}[/tex]
what factors of 52 add up to equal -8
Answers
Answer: 2x26 4x13 1x52
Step-by-step explanation:
Answer:
1 x 52 = 52.
2 x 26 = 52.
4 x 13 = 52.
Review #3 (TYPE ANSWERS HERE)
10 of 1510 of 15 Items
Question
POSSIBLE POINTS: 2
10) A student has a cup containing 5 green, 5 red, 5 yellow and 5 orange skittles. The student randomly takes a skittle out of the cup (and replaces it) 20 times. The results are:
Red: 3 times
Yellow: 7 times
Orange: 4 times
Green: 6 times
What is the relative frequency (experimental probability) of getting an orange skittle?
.
What is the theoretical Probability of getting an orange skittle?
Answers
An equilateral triangle has an altitude length of 33 feet. Determine the length of a side of the triangle.
Answers
Answer:
38.11 feet
Step-by-step explanation:
all three corners of an equilateral triangle are 60°
sin 60° = 33/x
0.8660 =33/x
x = 38.11 feet
Relation between the side and the altitude of the equilateral triangle can be given as,
[tex]a=\dfrac{2}{\sqrt{3} } h[/tex]
The length of the side of the equilateral triangle is 38.105 feet.
What is equilateral triangle?When all the three sides and all the three angle of a triangle are equal, then the triangle is known as Equilateral triangle.
Relation between the side and the altitude of the equilateral triangle can be given as,
[tex]a=\dfrac{2}{\sqrt{3} } h[/tex]
Here, [tex]a[/tex] is the side of the equilateral triangle and h is the altitude of the equilateral triangle
Given information-
Altitude of the equilateral triangle is 33 feet.
Put the value of altitude in above formula to find the length of the side of the equilateral triangle. Thus,
[tex]a=\dfrac{2}{\sqrt{3} } \times33\\a=38.105[/tex]
Thus the length of the side of the equilateral triangle is 38.105 feet.
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A coach is buying snacks for 22 players on a soccer match chip is a total of $77 to buy each player a bottle of water and energy bar the price of one energy bar is two dollars
Answers
The question is incomplete:
A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to buy each player a bottle of water and an energy bar. The price of one energy bar is $2. Let w equal the price of a bottle of water. Write an equation that represents the situation.
Answer:
x=44+22w, where
x is the total amount paid
w is the price of a bottle of water
Step-by-step explanation:
With the information provided, you can say that the total amount paid is equal to the result of multiplying the price per energy bar for the number of energy bars purchased plus the result of multiplying the price per bottle of water for the number of bottles of water:
price per energy bar= $2
number of enrgy bars= 22
price per bottle of water= w
number of bottles of water= 22
x=(2*22)+(w*22)
x=44+22w, where
x is the total amount paid
w is the price of a bottle of water
Select the correct answer.
What is the solution set of y = x² + 2x + 7 and y = x + 7?
A.
{(0, 7), (-1, 6)}
B.
{(0, 7), (-7, 0)}
C.
{(0, 7), (1, 8)}
D.
{(-2, 0), (4, 0)}
Answers
Answer:
c
Step-by-step explanation:
Help, Grades due Friday!
Two triangles are similar. The lengths of the sides of the smaller triangle are 3 inches, 5 inches, and 6 inches, and the length of the longest side of the larger triangle is 18 inches. What is the perimeter of the larger triangle?
A.
14 inches
B.
18 inches
C.
24 inches
D.
42 inches
Answers
Answer:
42 (d)
Step-by-step explanation:
the longest side of the smaller one is 6, each side of the larger one is just 3x the length of the smaller side. I hope that makes sense, it's just a ratio. Hope this helped! Good luck!
Answer:
The perimeter of the larger triangle is 42 inches.
Step-by-step explanation:
Since the question mentions that the two triangles are similar, we must establish proportions using what we already know.
Smaller triangle: 3 + 5 + 6 = 14
Larger triangle: x + y + 18 = perimeter
Determine the GCF (greatest common factor):
The GCF is 3.
Now, subsitute the values for x and y by solving via the GCF.
Larger triange: 9 + 15 + 18 = perimeter
9 + 15 + 18 = 42
Hope this helps; have a wonderful day!
Find the magnitude and direction of r+u
please help !!
Answers
Answer:
a.
5.4 cm; 133 degrees
Step-by-step explanation:
hope this helps
Can someone solve these rational expressions showing work thanks
Answers
Answer:
[tex]\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}=\frac{1}{2+x}[/tex]
Step-by-step explanation:
[tex]\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{x-5+2}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-5+2=-3[/tex]
[tex]=\frac{x-3}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]
[tex]=\frac{1}{2+x}[/tex]
Help solve this I’m not sure if my answer was right. Pythagorean theorem.
Answers
Answer:
C. since 8, 15, 17 are pythagorean triples
How do you find radius from cercumference?
(if at all Possible)
Answers
Answer:
r = C/2π
Step-by-step explanation:
You just rearrange the Circumference formula so you can find r.
Circumference formula:
C = 2πr
To find r, you multiply 1/2π on both sides of the equation so you can isolate r:
r = C/2π
In the Diagram, PA and PB are tangent to circle O at A and B, respectively. Diameter BOD and chord AC intersect at E, mCB=160, and m<APB=40
Find
a.mADCB
b.mAB
c.mCD
d.mDA
e.mDEC
f.mPAC
g.mPBD
h.mPBA
Answers
t-shirt costs $12 A pair of shorts costs $25 Amira plans on spending no more than $160 and wants to buy more than 5 items.
Answers
Answer:
5 shirts and 4 pairs of shorts
Step-by-step explanation:
160-1 set (12+25=37)=123
123-1 set=86
86-37=49
49-37=12
12-1 t-shirt=0
The straight line PQ with P(1,6) and Q(-6, 1). PQ is mapped onto P'Q' by a reflection in the line = 2. What are the coordinates of P
Answers
Answer:
[tex]P' = (1,-2)[/tex]
Step-by-step explanation:
Given
[tex]P = (1.6)[/tex]
[tex]Q = (-6,1)[/tex]
Reflection over: [tex]y = 2[/tex]
Required
Determine the coordinates of P'
From the given coordinates, the y coordinates of P is 6 and the line of reflection is at y = 2
Since we are to reflect over y = 2, only the y coordinate of P will be affected.
The idea behind reflecting a point over a line is to have an equal distance between [the original point & the line of reflection] and [the new point & the line of reflection]
So, what to do is:
First, calculate the difference between the y coordinates of P and the line of reflection.
The y coordinate of P is 6 and the line of reflection is at y = 2.
So, the difference is: 6 -2 = 4
Next, subtract the calculated difference from the line of reflection to get the y coordinate of P'
y coordinate of P' = 2 - 4 = -2
Hence, the coordinate of P' is: (1,-2)
I really need some help with this question
Answers
Answer:
inverse
Step-by-step explanation:
inverse
hope this helps
y = 8 ∙ 3^x for x = 4 20 POINTS
Answers
Answer:
648
Step-by-step explanation:
8×3^4=648
8×81=648
Number of Amusement Park Visits A 2-column table with 5 rows titled Number of Amusement Park Visits. Column 1 is labeled Visits with entries 1, 2, 3, 4, 5. Column 2 is labeled Tally with entries 4, 7, 3, 4, 2. You asked amusement park visitors the question “How many amusement parks have you visited this summer?” The tally table shows the results. Which number line would be best to use to create a dot plot of the set of data? a number line from 0 to 4 a number line from 1 to 5 a number line from 2 to 7 a number line from 0 to 7
Answers
Answer:
B
Step-by-step explanation: let me know if this is wrong
Answer:
its b
Step-by-step explanation:
well the person above me is correct he should get brainlies
what is 8+2 plesseeee
Answers
Answer:
10
Step-by-step explanation:
the is answe is 10 sheeesh
PLSSSS HELPPPP 30 POINTSSSS
Jaylon spent $27.60 of the $80 he got for his birthday. What percent of his money did spends
Answers
Answer:
35.4%
Step-by-step explanation:
(100/80) x 27.6
basically 1 of 80 is 1.25 and multiply 1.25 times the money jaylon spent sorry i am really bad at explaining only good at solving
Answer:
34.5%
Step-by-step explanation:
to find the percent of money that was spent, you turn it into a fraction-
27.60/80
=0.345
then to get the percent you multiply-
0.345*100
=34.5%
good luck :)
i hope this helps
brainliest would be highly appreciated
have a nice day!
5
Marie was hiking. She started at
10 feet above sea level and
then traveled up a mountain,
reaching 90 feet above sea
level. How many feet must she
descend to be at sea level?
athy
Answers
Answer:
90
if she's at 90ft above sea level she just needs to go back down 90ft to get to sea level
Find the 88 term of the arithmetic sequence 4,-1,-6
Answers
Answer:
an = a1 + d(n - 1)
a88 = 4 + (-5)(88 - 1)
a88 = 4 + (-5)(87)
a88 = 4 - 435
a88 = -431
So, the 88th term of the arithmetic sequence is -431.
Find the measure of angle H
Answers
Answer:
80
Step-by-step explanation:
All triangle angles add up to 180 so:
4x - 20 + 2x + 2x = 180
8x - 20 = 180
8x = 200
x = 25
<H:
4x - 20
4(25) - 20
100 - 20
80
In circle o,find the value of x, rounded to the nearest tenth.
Answers
Answer:
x = 6
Step-by-step explanation:
The line marked 16 is a chord.The line marked 20 is a diameter.1/2 the diameter is a radius.The radius = 1/2 20 = 10The value x meets 16 at it's midpointIt is given to be 90 degrees.The part of the radius meets the chord at its midpoint.The meeting point to the circumference is 8 units.The Pythagorean Theorem applies.10^2 = 8^2 + x^2100 = 64 + x^2100 - 64 = x^236 = x^2x = 6Describe an Angle Bisector
Answers
Answer:
An angle bisector is a straight line that divides the angle into two equal parts.
Step-by-step explanation:
Answer:
The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter.
Step-by-step explanation:
please mark me as brainlest
Simplify the expression
(3x4 + 9x3 – 7x + 15) + (-6X4 – 8x2 + 5x – 3)
Answers
Answer:
If the numbers next to the "x" are "carroted" ( ^ ) then the answer is
-3x^4 + 9x^3 -8x^2 -2x +12
Step-by-step explanation:
Basically, you just add the like terms together.
Scuba diver dives at a rate of 20 ft./min. If the diver starts at the surface what is the depth of the diver after 4 minute
Answers
Answer:
80 ft
Step-by-step explanation:
Distance = rate x time. Therefore, 20 ft / min x 4 min = 80 ft.