Question

1. a hiker is standing 220 feet from the base of a hill. the angle of elevation from where he is standing to the top of the hill is 29°. how tall is the hill?

Explanation:

Step1: Use the tangent function

In a right - triangle (formed by the hiker's distance from the base of the hill, the height of the hill, and the line of sight to the top of the hill), the tangent of an angle of elevation $\theta$ is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 29^{\circ}$, the adjacent side $x = 220$ feet, and the opposite side $y$ (height of the hill) is what we want to find. So, $\tan(29^{\circ})=\frac{y}{220}$.

Step2: Solve for $y$

We can rewrite the equation from Step 1 as $y = 220\times\tan(29^{\circ})$. We know that $\tan(29^{\circ})\approx0.5543$. Then $y=220\times0.5543$.

Step3: Calculate the value of $y$

$y = 220\times0.5543=121.946\approx122$ feet.

Answer:

The height of the hill is approximately 122 feet.