Question

An observer stands on the bank of a river, and looks directly across the river to a tree on the opposite bank. The angle of elevation from the feet of the observer to the top of the tree is 44 degrees. if the tree is 22ft tall how wide is the river

Answer 1

The width of the river is 22.8

Answer 2

Explanation:

First that all, notice that this is a trigonometry problem. therefore we have to use formulas that we know

Ec.1. Sin(β) = opposite/Hypotenuse

Ec.2. Cos(β)= adjacent/ Hypotenuse

β is the anlge of elevation from the feet of th eobserver to the top of the tree. (44)

the opposite is the hight of the tree (22ft)

so we need to find the the Adjacent that represent the width of the river.

using Ec.2 I get: adjacent(River's width) = Cos(β) x Hypotenuse.

We do not know the value of the hypotenuse, but we can calculate with Ec. 1

Hypotenuse = opposite / Sin(β)

= 22ft / sin(44)

=1242.8 ft

Now we know the value of the Hypotenuse, we can use Ec.2 to find the width of the river

Adjacent(River's widthe)= Cos(44) x 1242.8 ft

= 1242.6ft

the width of the river is 1242.6 ft