Question

the angle of elevation to a nearby tree from a point on the ground is measured to be 64°. how tall is the tree if the point on the ground is 26 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use tangent function

In a right - triangle (formed by the tree, the ground, and the line of sight), the tangent of an angle of elevation $\theta$ is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 64^{\circ}$, the adjacent side $a = 26$ feet, and the opposite side is the height of the tree $x$. So, $\tan(64^{\circ})=\frac{x}{26}$.

Step2: Solve for $x$

We know that $\tan(64^{\circ})\approx2.0503$. Then, $x = 26\times\tan(64^{\circ})$. Substitute the value of $\tan(64^{\circ})$: $x=26\times2.0503$.

$$x = 53.3078$$

Answer:

$53.3$ feet