1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kolezko [41]
3 years ago
13

From a point 100 m from a building the angles of elevation of the top and bottom of a flagpole atop a building are 54.5 degrees

and 51.8 degrees, respectively. How tall is the flagpole?
Mathematics
1 answer:
AnnZ [28]3 years ago
4 0

Answer:60ft

Step-by-step explanation:The height of the flagpole is approximately  

60

feet.

Explanation:

Always try to draw a diagram.

enter image source here

We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.

Since the angle in the corner of the larger right triangle measures  

42

˚

, the top angle in this triangle measures  

180

˚

−

90

˚

−

42

˚

=

48

˚

.

By basic trig ratios, we can find the height of the building with the flag pole on top, call it  

H

.

tan

42

˚

1

=

H

500

H

=

500

tan

42

˚

I would keep it in exact form until the last step.

We now devise an expression for the height of the building (without the flag pole). Call it  

a

tan

38

˚

1

=

a

500

a

=

500

tan

38

˚

We can now state that

h

=

H

−

a

h

=

500

tan

42

˚

−

500

tan

38

˚

h

≈

59.559

≈

60

feet

Hopefully this helps!

Answer link

EET-AP

Apr 10, 2017

The flagpole is  

60

f

t

in height to the nearest foot.

Explanation:

1) The flagpole is on top of a building.

2)Angles of elevation both measured from point  

500

f

t

from building

3) Angle of elevation to the top of building is  

38

d

e

g

4) Angle of elevation to the top of flagpole is  

42

d

e

g

The information above will provide us with two right angle triangles, one smaller one inside a larger one.

Both will have a base of  

500

f

t

.

The smaller triangle will have a base angle  

β

of  

38

deg opposite the  

90

deg, and the larger triangle will have a base angle  

β

of  

42

deg.

From this information we can find the heights of the building and the building + pole using the definition of the tangent of the two base angles  

β

:

tan

(

β

)

=

o

p

p

a

d

j

where the  

o

p

p

is the height and the  

a

d

j

is the  

500

f

t

o

p

p

(

b

u

i

l

d

)

=

tan

(

38

)

⋅

(

500

f

t

)

=

390.6

f

t

=

height of building

o

p

p

(

f

l

a

g

)

=

tan

(

42

)

⋅

(

500

f

t

)

=

450.2

f

t

=

height of building + pole

Then to the nearest foot the height of the flagpole is:

450.2

f

t

−

390.6

f

t

=

60

f

t

You might be interested in
The grid shows the positions of a subway stop in your house does subway stop is located at The grid shows the positions of a sub
professor190 [17]

Answer:

I need a picture to solve...

Step-by-step explanation:

3 0
3 years ago
Factor the expression below.
Genrish500 [490]

Answer:

A. (6x + 7)(6x - 7)

Step-by-step explanation:

use difference of squares, which says a^2 - b^2 =(a+b)(a-b)

take the square roots of the two numbers, 6x and 7, and use them as a and b

8 0
1 year ago
One third of a number Y
vampirchik [111]

Answer:

⅓y

Step-by-step explanation:

\frac{1}{3}  \times y \\  =  \frac{1}{3} y

4 0
3 years ago
Write an equation in point-slope form of a line with a slope of –4 that goes through the point J(–5, 6).
Fittoniya [83]
The equation is y = -4x + 26.
5 0
3 years ago
Solve for x. Your answer must be simplified. -7x > 10
andre [41]
The answer to this is x < -10/7
5 0
3 years ago
Other questions:
  • Which formula is used to find the volume of a cone ​
    6·2 answers
  • Describe different ways that you can show a story problem
    5·1 answer
  • What is the answer really need it my moms checking it when she gets back
    10·1 answer
  • 875,932,461,160 what digit is in the hundred-millions place of this number.
    10·1 answer
  • NIKKI'S BACKYARD IS THE SHAPE OF A RECTANGLE. THE LENGTH IS 27 FEET. THE WIDTH IS ONE THIRD THE LENGTH PLUS 4 FEET. WRITE AND EV
    14·2 answers
  • Need help with algebra 2!
    5·1 answer
  • ~I ~ need ~ help ~ once ~ again~
    8·1 answer
  • What is the distance along the unit circle between any two successive 8th roots of 1?
    8·1 answer
  • The function g(x) undergoes a vertical stretch of 2, a horizontal shift to the right 3 units, and a vertical shift up 1 to becom
    15·1 answer
  • FREE BRAINLIEST QUICK WHATS THE BEST WAY TO FAKE BEING SICK SO YOU DON'T HAVE TO GO TO SCHOOL
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!