Question

The angle from a stake in the ground to the top of a tree is 60 degrees. If the height of the tree is 40 feet, what is the distance from the stake to the bottom of the tree (the distance along the gound) in feet?

Answer 1

@vocaloid

Answer 2

This question is pretty self-explanatory if you can see it visually.



The angle is where the stake on the ground is and the tree is opposite of the angle which makes 40 the opposite.

Out of the three trig functions, we will use tangent here because we know the opposite and we are trying to find the adjacent (which is the distance along the ground).

tangent = opp / adj

opposite - 40
adjacent - x


So lets plug in that we know and solve for what we dont know.
\[\tan 60º = \frac{ 40 }{ x }\]
\[\frac{ 40 }{ \tan60 }\]

When we put the value above on a calculator, the final answer you should get is `"23.1"`

That means, the distance along the ground from the stake to the tree is `23.1 feet` (23 is rounded to the nearest whole number).