trigonometry

Question

Help me and show work please

 

From a boat on the lake, the angle of elevation to the top of a cliff is 27°57'. If the base of the cliff is 128 feet from the boat, how high is the cliff (to the nearest foot)?

Answer 1

Using SOHCAHTOA we can figure this problem out.

 

First we need to convert minutes to decimals. 

To do this, we divide 57'/60 min = .95

This makes θ = 27.95°

 

We know that θ=27.95° and A=128

to find O (the height of the cliff) , we use Tan(θ)=O/A

 

so Tan(27.95°) = O/128

O = 128Tan(27.95°)

O = 67.92 ft

 

Height of the cliff ≈ 68 ft.

Answer 2

Hi Sasha,

 

Let the height of the cliff be x foot. From the basic trigonometry we will have,

 

tan (27°57') = x / 128

 

x= 128 * tan(27°57')

 

x = 128 * 0.53 = 67.9 foot