A person whose eye level is 11 ft above the ground is looking at a building. The angle of elevation to the top of the building is 22 degrees and the angle of depression to the bottom of the building is 34 degrees. What is the height (in feet) of the building? Round your answer to the nearest foot.

Answers

Answer 1

Answer:

The building has a height of 14 feet.

Step-by-step explanation:

At first we construct the geometrical diagram respective to the person-building system, whose result can be seen in the attached image. We proceed to describe each variable:

[tex]h[/tex] - Height of the eye level above the ground, measured in feet.

[tex]H[/tex] - Height of the building, measured in feet.

[tex]\alpha[/tex] - Angle of elevation, measured in sexagesimal degrees.

[tex]\beta[/tex] - Angle of depression, measured in sexagesimal degrees.

[tex]r[/tex] - Distance between eye level and the bottom of the building, measured in feet.

[tex]r'[/tex] - DIstance between eye level and the top of the building, measured in feet.

By using trigonometric ratios and functions we find that height of the building is represented by the following formula:

[tex]H = r\cdot \sin \beta + r'\cdot \sin \alpha[/tex] (Eq. 1)

But [tex]r[/tex] and [tex]r'[/tex] can be obtained by these expressions:

[tex]r = \frac{h}{\sin \beta}[/tex] (Eq. 2)

[tex]r' = \frac{r\cdot \cos \beta}{\cos \alpha}[/tex] (Eq. 3)

By (Eq. 2) in (Eq. 3):

[tex]r'= \frac{h}{\cos \alpha \cdot \tan \beta}[/tex] (Eq. 3b)

Now, we expand (Eq. 1) by (Eqs. 2, 3b):

[tex]H = h + h \cdot \tan \alpha \cdot \tan \beta[/tex]

[tex]H = h\cdot (1+\tan \alpha \cdot \tan \beta)[/tex] (Eq. 4)

If we know that [tex]h = 11\,ft[/tex], [tex]\alpha = 22^{\circ}[/tex] and [tex]\beta = 34^{\circ}[/tex], the height of the building is:

[tex]H = (11\,ft)\cdot (1+\tan 22^{\circ}\cdot \tan 34^{\circ})[/tex]

[tex]H = 13.998\,ft[/tex]

The building has a height of 14 feet.

A Person Whose Eye Level Is 11 Ft Above The Ground Is Looking At A Building. The Angle Of Elevation To

Related Questions

What is tje equation of the function?

Answers

Answer:

It is relatively easy to determine whether an equation is a function by solving for y. When you are given an equation and a specific value for x, there should only be one corresponding y-value for that x-value. For example, y = x + 1 is a function because y will always be one greater than x.

Step-by-step explanation:



A bacteria colony starts with 5 bacteria at the beginning and triples every hour. How would

you write an explicit equation to model this situation?

A. f(x) = 3.5*

B. f(x) = 3x + 5

C. f(x) = 5x + 3

D. f(x) = 5.3%

Answers

Answer:

B. f(x) = 3x + 5

Step-by-step explanation:

Initial amount of bacteria N0 = 5 bacteria's

If the triple every hour,

The increase in bacteria in the colony after x hour will be 3*x =3x

x is the amount of hour.

Total amount of bacteria in the colony after x hour will be N0 + 3x

Let f(x) be the total amount of bacteria in the colony after x hour

f(x) = N0+3x

Since N0 = 5

f(x) = 5+3x

Re-arrange

f(x) = 3x + 5

Hence an explicit formula to model the equation is f(x) = 3x + 5

y = 1.6x + 48
Based on the equation, what is the approximate shoe size for a man having a height of 60 inches?
A. 7 1/2
B. 10 1/2
C. 12
D. 14

Answers

The answer is C 10 ... 1/2

5*2+1+1= what I know the answer but people need points

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

10+1+1

Number 8 please!!!!!!

Answers

Answer:

the answer is a= -20

can you also please mark me as brainliest?

thanks

f=2 :) well that’s what I got from working it out

Find the quotient.
42+2 = (-822-2)

Answers

Answer:1606

Step-by-step explanation:

The perimeter of a rectangle is 54 feet. The width is 1 less
than the length. What are the dimensions of the rectangle?

Answers

Step-by-step explanation:

length=x

width=x-1

x + x + (x-1) + (x-1) = 54

4x - 2 = 54

4x = 56

x = 14 ft

x = 14 ft

x - 1 = 14 - 1 = 13 ft

x = 14 ft

x - 1 = 14 - 1 = 13 ft

Perimeter= x + x + (x-1) + (x-1)

54 ft = 14 + 14 + (14 - 1) + (14 - 1)

54 ft = 28 + (13 +13)

54 ft = 54 ft

SOMEONE HELP
how many serving were in the Container?

Answers

...................15?

Answer: B) 6 servings

====================================================

Explanation:

5 & 1/3 is the mixed number with 5 as the whole part and 1/3 as the fractional part

Let's convert to an improper fraction

5 & 1/3 = 5 + 1/3

5 & 1/3 = 5*(3/3) + 1/3

5 & 1/3 = 15/3 + 1/3

5 & 1/3 = (15+1)/3

5 & 1/3 = 16/13

The mixed number 5 & 1/3 is equivalent to the improper fraction 16/3

-------------------

Each serving is 7/8 cup

x of these servings is (7/8)x

x is the number of servings in a full container, so

(7/8)x = 16/3

x = (16/3)*(8/7)

x = (16*8)/(3*7)

x = 128/21

x = 6.0952 approximately

x = 6 when rounding to the nearest whole number

So the container is about 6 servings.

The sum of one nickel and one dime is what fraction of a U.S. dollar?
3/20
15/20
15/10
3/100

Answers

Answer:

3/20

Step-by-step explanation:

15 cents is 15/100. Just simplify the fraction :3

Answer:

I guess 3/20 not sure

I am really sorry If I got the answer wrong

If (-3)^5 = 1/x, what is the value of x?

Answers

Step-by-step explanation:

(-3)^5 = 1/x

x = 1 ÷ (-3)^5

x = 1/ -243

x = -1/243

HELP URGENT!!!!!!!!!!!!!!!!!

Answers

Answer:

c=1,1  d=3,1  e=3,3

Step-by-step explanation:

3. Do the following represent a function? Explain why or why not for each.​

Answers

Answer:

No and No

Step-by-step explanation:

Two x-intercepts match up to more than one y-intercept.

Given m angle7=38^ and m angle10=102^ find the measure of each missing angle

please show work to help me​

Answers

[tex]\angle 1 = 78\\\angle 2 = 102\\\angle 3 = 78\\\angle 4 = 102\\\angle 5 = 38\\\angle 6 = 142\\\angle 7 = 38\\\angle 8 = 142\\\angle 9 = 78\\\angle 10 = 102\\\angle 11 = 78\\\angle 12 = 102\\\angle 13 = 38\\\angle 14 = 142\\\angle 15 = 38\\\angle 16 = 142[/tex]

The measure of the angles will be ∠1 = 78°, ∠2 = 102°, ∠3 = 78°, ∠4 = 102°, ∠5 = 38°, ∠6 = 142°, ∠7 = 38°, ∠8 = 142°, ∠9 = 78°, ∠10 = 102°, ∠11 = 78°, ∠12 = 102°, ∠13 = 38°, ∠14 = 142°, ∠15 = 38°, and ∠16 = 142°

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The type of angles is given below.

Two angles are said to be supplementary angles if their sum is 180 degrees.If two lines are parallel then the third line. The corresponding angles are equal angles.When two lines intersect, then their opposite angles are equal.

The measure of angle 7 is 38°. Angles 7 and 8 are supplementary angles.

∠7 + ∠8 = 180°

38° + ∠8 = 180°

∠8 = 142°

The measure of angle 10 is 102°. Angles 9 and 10 are supplementary angles.

∠9 + ∠10 = 180°

102° + ∠9 = 180°

∠9 = 78°

Then the measure of the remaining angles will be

∠1 = 78°

∠2 = 102°

∠3 = 78°

∠4 = 102°

∠5 = 38°

∠6 = 142°

∠7 = 38°

∠8 = 142°

∠9 = 78°

∠10 = 102°

∠11 = 78°

∠12 = 102°

∠13 = 38°

∠14 = 142°

∠15 = 38°

∠16 = 142°

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

1. A.9(A) Given the following graph of an exponential function, which
inequality best represents the range of the graph?
*​

Answers

Answer:

The Renaissance set the principle that "Man is the measure of all things". As a consequence, there was a growing interest in the development of humankind in all fields. In order for this to happen, improvements in education and intelligence were crucial. As a product of this growing importance of education, that Humanism was founded. Humanism is known as a stance that emphasizes the value of all human beings.

Step-by-step explanation:

sorry i couldnt actually help      i need brainly points

he theater club is hosting a one-act competition to raise $1,220 for new costumes. It plans to sell tickets for $8 each and would like to earn within $100 of its goal. This is the equation representing this situation, where t is the number of tickets sold: |8t − 1,220| = 100. Type the correct answer in each box. Use numerals instead of words. To earn within $100 of its goal, the theater club needs to sell a minimum of tickets and a maximum of tickets.

Answers

Answer:

i think that your suppose to divide add and subtracct.

Step-by-step explanation:

Hope this helps.

Answer:

140

165

Step-by-step explanation:

To solve the absolute value equation, first rewrite the equation as two separate equations equal to -100 and 100:

8t − 1,220 = -100 8t − 1,220 = 100

8t = 1,120 8t = 1,320

t = 140 t = 165

To earn within $100 of its goal, the theater club needs to sell a minimum of 140 tickets and a maximum of 165 tickets.

Can someone help me please?

Answers

the answer is b, 3.50 dollars per gallon
the answer is b to this question... $3.50 per gallon is the answer!!

Question 1*
1 point
For questions 1-5, let f(x) = x2 +6x + 7, g(x) = 8x2 – 2, h(x) = 3x + 4, and
k(x) =
x-3
2x+1
1.
Evaluate f(2) - g(2). k(2)

Answers

Given expressions;

     f(x) = x² + 6x + 7

     g(x) = 8x² - 2

     h(x) = 3x + 4

     k(x) = x - 3

Find  f(2) - g(2). k(2)

f(2) = 2² + 6(2) + 7 = 23

g(2) = 8(2)² - 2 = 30

k(2) = 2 - 3 = -1

Now,  f(2) - g(2). k(2) = 23  - (30)(-1)

                                  = 53

The solution to the problem is 53

25 pts! Who wants brainliest? answer this question

Answers

Answer:

The answer is 7root 5

Step-by-step explanation:

Ms. Arango gave his daughter 50 chocolate bars to give to her friends
at her birthday party. She gave 3 chocolates to each of her friends and still
had 2 chocolates left. Write an equation to determine the number of
friends (f) at Mr. Arango's daughter's party. *

Answers

Answer:

Ans: 16

Step-by-step explanation:

50-2=48

48/3=16 friends

Each day, Kyle reads 30 pages of a 450-page book. Write a linear equation to represent the number of pages Kyle has left to read after x.

a. Write the linear equation in slope-intercept form.



b. How many days will it take Kyle to finish the book?

Answers

Answer:

y=-30x+450

if she reads 30 pages every day it will take 15 days

The length y of a rectangle is four less than three times the width x. The perimeter of the rectangle is 16 cm.

Answers

Answer:

y = 1 cm

x = 7 cm

Step-by-step explanation:

x = 3y + 4

perimeter = 2 * ( y + x ) = 16

x + y = 8 by using x = 3y + 4

y + 3y + 4 = 8

4y = 4

y = 1

1 + x = 8

x = 7

y = 1 cm

x = 7 cm

Chris earns a fixed amount of money every month. At the end of 2 years, Chris had earned $86,688.
He earned $_____ each year.
He earned $____every month.

Answers

He earned $43344 each year
He earned $ 3612 every month

can someone plz help me with this math equation!

Answers

Answer:

[tex]2x^3-7x^2-10x+4+\frac{1}{x+1}[/tex]

Step-by-step explanation:

Hey this is long division polynomials, my work is a little confusing and I see that you do not need to show step so ill skip it.

If you don't understand I recommand search a video on it

<3

Red

Pentagon ABCDE and Pentagon A''B''C'D''E are shown on the coordinate plane below.

which two transformations are applied to Pentagon ABCDE to create A"B"C"D"E"?

A) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis

B) Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the x-axis

C) Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis

D) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x-axis​

Answers

Answer:

D) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x-axis​

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, dilation and translation.

If a point X(x, y) is translated a units right and b units down, it new location is X'(x + a, y + b)

If a point X(x, y) is reflected across x axis, it new location is X'(x, -y)

Pentagon ABCDE is at A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), E(-2, 4) while pentagon A"B"C"D"E" is at A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), E"(6, -6)

If pentagon ABCDE is Translated according to the rule (x, y) → (x + 8, y + 2), the new points would be A'(4, 7), B'(2, 6), C'(3, 3), D'(6, 4), E'(6, 6). If a reflection across the x axis is the done, the new points are A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), E"(6, -6)

Identify the values for the elements in the augmented matrix: A = a11 a12 a13 a21 a22 a23 a11 = a12 = a13 = a21 = a22 = a23 =

Answers

Answer:

a11= 3

a12= 7

a13= 20

a21= 1

a22= -4

a23= 9

Step-by-step explanation:

the answer on edge 2020

Answer:

A11 = 3, A12=7, A13 = 20, A21 = 1, A22 = -4, A23 = 9

Step-by-step explanation:

EDGE 2023

1). y= 1/5x + 1
2). y= 1/5x
3). y= 5x - 1
4). y= -1/5x

Answers

The answer is the 2nd one… y=1/5x

Find the x- and y-intercepts of the graph of the linear equation 3x+6y=24.

Answers

Answer:

y=0,4 and x=8,0

The x and y-intercept of the linear equation 3x + 6y = 24 will be (8,0) and (0,4) respectively.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given linear function,

3x+6y=24

At x-intercept, y = 0

3x = 24

x = 8 thus it will be (8,0).

At y-intercept , x = 0

6y = 24

y = 4 thus it will be (0,4)

Hence "The linear equation 3x + 6y = 24 will have x-intercepts of (8, 0) and (0, 4) correspondingly".

For more about the linear function,

brainly.com/question/21107621

#SPJ2

How many cups of red paint should be added to 1 cup of white paint?

Answers

Answer:

3/7

Step-by-step explanation:

Im pretty sure it's correct

The answer is 3/7 of paint should be added

Which operation should you perform first when you simplify 175 − ( 8 + 45 ÷ 3 ) × 7?

Answers

Answer:

Divide 45 and 3

You should get 15

Add 15 to the eight

You should have got 23

Multiply 23 and 7

You should get 161

subtract it from 175

you should get 14

There are 4 pints of green paint in a gallon bucket. The paint is made from equal amounts of yellow paint and blue paint. To create a different shade of green, the mixture needs to be 80% yellow. How many pints of yellow paint need to be added to the bucket to make the mixture 80% yellow? Brandon says to get that shade of green, 6 pints of yellow paint need to be added to the bucket. Bianca says that won't work. In two or more complete sentences, explain who is correct and why. In your explanation, include the calculations to support the correct answer.

Answers

Answer:

Brandon is correct.

Step-by-step explanation:

Initially, there id 4 pints of green paint in the bucket.

As the green paint is made from equal amounts of yellow paint and blue paint, so, the initial amount of yellow and blue paint in the bucket  is 2 pint each.

Let x pints of yellow paint to be added to the bucket to make the desired shade.

Total amount of the paint in the bucket, after addition of [tex]x[/tex] pints of yellow color become [tex]4 + x[/tex] pint, in which the ampunt of yellow color is [tex]2+x[/tex] pints.

As, the ampunt of yellow color is 80% of the total amount of the mixture, so

[tex](4+x)\times 80\%=2+x[/tex]

[tex]\Rightarrow (4+x)\times \frac{80}{100}=2+x[/tex]

[tex]\Rightarrow 4(4+x)=5(2+x)[/tex]

[tex]\Rightarrow x=6[/tex]

So, 6 pints of yellow paint to be added to the bucket to make the desired shade.

Hence, Brandon is correct.

Answer:

Brandon is correct that the mixture needs 6 more pints of yellow paint.

50%(4 pints) + 100%(x pints) = 80%(4 + x pints)

2 + x = 3.2 + 0.8x

0.2x = 1.2

x = 6

Bianca is correct because adding the 6 pints won't fit in the gallon bucket. Adding 6 pints of yellow to the original 4 pints of green is 10 pints, which will not fit in the 1-gallon bucket. (1 gallon = 8 pints)

Step-by-step explanation:

used this for my test and it was right

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