Question

WORTH 20 POINTS, PLEASE ANSWER CORRECTLY! (THE ANSWER IS NOT 26.005)

A person noted that the angle of elevation to the top of a tree was 65 degrees at a distance of 11 feet from the tree. Using the diagram approximate the height of the tree.

5.128 feet

26.005 feet

12.14 feet

23.590 feet

Answer 1

23.590 feet

Explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides of a right triangle:

Tan = Opposite/Adjacent

Here, that means ...

tan(65°) = height/(11 ft)

Multiplying by 11 ft, we get ...

height = (11 ft)tan(65°) ≈ 23.5896 ft

height ≈ 23.590 ft