Question

Matthew has been asked to determine the height of a tree. He measured the height from the ground to his eye and found that it was 5 feet. He used a protractor to measure the angle between the horizontal and his line of sight to the top of the tree. He found that angle to measure 70 degrees He also determined his distance from the tree and found that it measured 12 fect. Use the information to determine the height of the tree .

Answer 1

Height of the tree is
`37.88` feet

Explanation:

The height of the tree is equal to the sum of distance from ground level to eye level and distance between eye level to the top level of the tree.

Height of the tree
`= 5 + X`

`tan \Theta =` Perpendicular / Base

`tan\Theta = (X)/(12) \\X = 12 * tan70\\X= 12 * 2.74\\X = 32.88`

Total height of tree
`= 5 + X = 5 + 32.88 = 37.88` feet