Question

an alligator forms an angle of elevation of 31° from the ground to a mans face. the diagonal distance from the alligator to the mans face is 20 feet. what is the horizontal distance between the alligator and the man? 30.8 10.3 12 17.1 18 20.6

Explanation:

Step1: Use cosine function

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 31^{\circ}$ and the hypotenuse is $20$ feet. Let the horizontal distance (adjacent side) be $x$. So, $\cos(31^{\circ})=\frac{x}{20}$.

Step2: Solve for $x$

We know that $\cos(31^{\circ})\approx0.8572$. Then $x = 20\times\cos(31^{\circ})$. Substitute the value of $\cos(31^{\circ})$: $x=20\times0.8572 = 17.144\approx17.1$.

Answer:

$17.1$