Please solve this?

Question

1. You are standing 10 ft away from a tree. The angle of elevation from your foot to the top of the tree is 65 degrees. How tall is the tree? 

 

2. A boy scout on on top of a 1700-ft-tall mountain spots a campsite. If he measure the angle of depression at 35 degrees, how far is the campsite from the foot of the mountain?

Answer 1

Hi Sydney,

 

1) This describes a right triangle with angles 65 and 25 degrees.

tan(65deg) = height of tree / 10

height of tree = 21 ft (rounded to the nearest whole number) 

 

2) I am assuming that the campsite is located at the same level as the foot of the mountain. 

Angle of depression is the angle formed between the observer's horizontal and the line of sight. Then,

we have a right triangle whose side across from 35 degrees is the elevation of the boy scout and the other side is the distance of the campsite from the foot of the mountain. I will call that x.

 

tan(35 deg) = 1700/x

x = 2428 ft (rounded to the nearest whole number)