Question

Sarah sights the top of the Statue of Liberty at an angle elevation of 61 degrees. If Sarah is 5.5 ft tall and is standing 166 feet from the base of the statue, find its heigh. Draw a picture, then solving for the missing parts

Answer 1

we are given that

Sarah sights the top of the Statue of Liberty at an angle elevation of 61 degrees. If Sarah is 5.5 ft tall and is standing 166 feet from the base of the statue, find its heigh.

The picture has been attched

In the Triangle ABC we can write

`tan61=(x)/(5.5)\\ \\ x=tan61*5.5\\ \\ x=9.922 \approx 10`

Hence the Height of the statue
`= 10+5.5=15.5ft`

All the missing parts have been sketched in the diagram.

Answer 2

height of the statue = 299. 50 ft + 5.5 ft = 305.5 ft

Explanation:

The picture above illustrate Sarah's activities. The height of the statue can be computed below

Using SOHCAHTOA principle

tan 61° = opposite/adjacent

opposite = h

adjacent = 166 ft

tan 61° = h/166

cross multiply

h = 166 tan 61°

h = 166 × 1.8040477553

h = 299.47192738 ft

h ≈ 299. 50 ft

Since she is standing on the same level where the base of the statue spring from the height of the statue will be 299. 50 ft plus Sarah's height.

height of the statue = 299. 50 ft + 5.5 ft = 305.5 ft