Question

How much taller is one tree than the other?

Answer 1

Answer:

3.71

Step-by-step explanation:

The distance between the trees and the point is 50 meters. If the pictures are illustrated correctly, the tree on the left has an angle of elevation of 16, while the other tree on the right has an angle of elevation of 12.

Given one of the legs (b) of the triangle and also the degree, we can easily use the simple SOHCAHTOA method to solve this problem.

Note* SOHCAHTOA: sin(θ)=O/H cos(θ)=A/H tan(θ)=O/A

*θ means theta, which is the angle we choose to reference on.

In this case, we are looking for the length of the shorter legs (a), which is the opposite of theta (the angle 16 or 12), so we can call them the opposite (O) and the longer legs (b) the adjacent (A).

Now with everything labeled, let's first find the tree on the left:

We are going to use tan this time since we don't need to find the hypotenuse.

tan(16)=O/50 <== now use calculator

O=14.34 <== estimation
Now the tree on the right:

tan(12)=O/50

O=10.63

Don't forget the most important step: answer the problem!

14.34-10.63=3.71

Hope that helps!