Question

8.) john wants to measure the height of a tree. he walks exactly 100 feet from the base of the tree and looks up. the angle from the ground to the top of the tree is 33°. how tall is the tree?

Explanation:

Step1: Set up tangent - ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the tree be $h$. The adjacent side to the angle of elevation is the distance from the base of the tree ($100$ feet) and the opposite side is the height of the tree $h$. The angle of elevation $\theta = 33^{\circ}$. So, $\tan(33^{\circ})=\frac{h}{100}$.

Step2: Solve for $h$

Multiply both sides of the equation $\tan(33^{\circ})=\frac{h}{100}$ by $100$ to get $h = 100\times\tan(33^{\circ})$. Since $\tan(33^{\circ})\approx0.6494$, then $h=100\times0.6494 = 64.94$ feet.

Answer:

$64.94$ feet