Question

An ecologist wishes to find the height of a redwood tree that is on the other side of a creek, as shown in the figure below. From point A he finds that the angle of elevation to the top of the tree is 10.4°. He then walks 24.8 feet at a right angle from point A to point B. There he finds that the angle between AB and a line extending from B to the tree is 85.8°. What is the height h of the tree? (Round your answer to one decimal place.)

Answer 1

Answer:

The height h of the tree is 62.0 feet

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the length side AC

In the right triangle ABC

$tan(85.8^o)=\frac{AC}{AB}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the given value

$tan(85.8^o)=\frac{AC}{24.8}$

$AC=tan(85.8^o)(24.8)$

$AC=337.7\ ft$

step 2

Find the length side CD (height of the tree)

In the right triangle ACD

$tan(10.4^o)=\frac{CD}{AC}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the given value

$tan(10.4^o)=\frac{CD}{337.7}$

$CD=tan(10.4^o)(337.7)$

$CD=62.0\ ft$