Question

The naturalist views an elephant in the distance, but he doesn’t know how far away the elephant is from him. He takes a view to find the a 22 degree angle of elevation. He moves backwards from the elephant pacing off a distance of 27 feet. He takes a second view and determines a new angle of elevation of 11 degrees. How tall is the elephant? How far away was the naturalist when he first saw the elephant

Answer 1

Answer:

10.11 feet

Step-by-step explanation:

Let H ft be the elephant's height and x ft be the initial distance from naturalist to the elephant.

1. Naturalist takes a view to find the a 22 degree angle of elevation, then

$\tan 22^{\circ}=\dfrac{H}{x}.$

2. Naturalist moves backwards from the elephant pacing off a distance of 27 feet, the distance from naturalist to the elephant becomes (x+27) ft. He takes a second view and determines a new angle of elevation of 11 degrees. Then

$\tan 11^{\circ}=\dfrac{H}{x+27}.$

3. Solve the system of two equations:

$\left\{\begin{array}{l}\tan 22^{\circ}=\dfrac{H}{x}\\\tan 11^{\circ}=\dfrac{H}{x+27}\end{array}\right.\Rightarrow \dfrac{x+27}{x}=\dfrac{\tan 22^{\circ}}{\tan 11^{\circ}}\approx 2.0785,\\ \\ \\x+27=2.0785x,\\ \\1.0785x=27,\\ \\x\approx 25.0347\ ft.$

Then

$H=x\cdot \tan 22^{\circ}\approx 10.11\ ft.$