Question

the angle of elevation to a nearby tree from a point on the ground is measured to be 26°. how tall is the tree if the point on the ground is 91 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use the tangent function

The tangent of an angle in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 26^{\circ}$, the adjacent side is $91$ feet, and the opposite side is the height of the tree $x$. So, $\tan(26^{\circ})=\frac{x}{91}$.

Step2: Solve for $x$

Multiply both sides of the equation by $91$: $x = 91\times\tan(26^{\circ})$.
We know that $\tan(26^{\circ})\approx0.4877$. Then $x=91\times0.4877$.
$x = 44.4807$.

Answer:

$44.5$ feet