Question

I know the answer to this, (from other posts) but I need to understand how to work out the problem. From what I've read, the answer is A) 23.1 feet.
The problem: An ant looks up at an angle of 30 degrees to the top of a tree. If the ant is 40 feet from the base of the tree, what is the height of the tree, to the nearest tenth?

Answer 1

We're forming a triangle where the distance between the ant and the tree is the base (40ft), the angle is 30deg, and the height of the tree is the height of the triangle. We can find the answer using basic trig.

The other non-right angle in the triangle must have measure 60 degrees. We then use the law of sines where h is the height:
\[\frac{40}{\sin60} = \frac{h}{\sin 30} \implies h = \frac{40\sin 30}{\sin 60} = 23.09... \approx 23.1\]

Answer 2

we are assuming this to be a right triangle ....

Answer 3

If it isn't, we don't have enough information to answer the question without being told the value of the other angle.

Answer 4

*** An ant looks up at an angle of 30 degrees to the top of a tree. If the ant is 40 feet from the base of the tree,***

First, sketch the problem