Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 20∘

. How tall is the tree if the point on the ground is 92 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

`\\ \rm\rightarrowtail cot\theta=(B)/(P)`

`\\ \rm\rightarrowtail cot20=(92)/(P)`

`\\ \rm\rightarrowtail P=(92)/(cot20)`

`\\ \rm\rightarrowtail P=(92)/(2.7475)`

`\\ \rm\rightarrowtail P=33.49ft`

Answer 2

• 33.49 feet

Explanation:

This is about the right triangle, where 92 feet side is adjacent leg to 20° angle, x - height.

Use trigonometry to find the height

• x / 92 = tan 20°
• x = 92 tan 20°
• x = 33.49 feet (rounded)