Question

You are looking at the top of a building and thinking it would be great to make a zipline from the top to your current location. You measure the angle of elevation as 37 degrees and you are 123 feet from the base of the building . How long a zipline is needed if you are 6 feet tall ? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a foot.

Answer 1

Answer:

52 feet

Step-by-step explanation:

From the problem, we are given that the angle of elevation as 37 degrees and you are 123 feet from the base of the building. How long a zipline is needed if you are 6 feet tall?

Let us consider a triangle  

A

B

C

in which we have a line from  

A

to  

B

C

with a point named  

D

Given that  

D

C

=

152

foot and  

∠

D

A

B

=

28

∘

,

∠

C

A

B

=

39

∘

.

Now we have to find the height of the flagpole  

A

B

So, from the applying the tangent formula we get,

tan

(

39

)

=

B

C

A

B

A

B

=

(

B

D

+

D

C

)

0.809

A

B

=

(

100

+

D

C

)

(

0.809

)

(

equation 2

)

tan

(

28

)

=

B

D

A

B

A

B

=

100

(

0.531

)

(

equation 1

)

Now, we have two expressions for AB so we we equate both equations 1 and 2,

(

100

+

D

C

)

(

0.809

)

=

100

(

0.531

)

D

C

=

100

(

1.523

−

1

)

D

C

=

100

(

0.523

)

D

C

=

523

Therefore, the length of the zipline is  

52

feet.

Answer 2

AC approx 154ft

Step-by-step explanation:

COS 37 degrees = base/hypotenuse

0.7986=123/AC

AC=123/0.7986

=154.019534

AC approx 154ft