trig/pre cal

Question

A man with his eye level 6 feet above the ground is standing 3 feet away from the base of a 15-foot vertical ladder. If he looks to the top of the ladder, at what angle above the horizontal is he looking? (Round your answer to one decimal place.)

Answer 1

Hi Mark!

We can imagine if we drew this situation, you would end up with a right triangle. The base of the triangle would be 3ft. and the vertical leg would be 9ft. (15ft ladder - 6ft man). We then have the adjacent segment of the triangle (the base) and the opposite segment (the vertical leg or ladder). Using SOH CAH TOA, we have to use the tan function based on our known variables.

tan(theta)=Opposite/Adjacent

tan(theta)=9ft/3ft

tan(theta)=3

Now, use the inverse tan function (tan^-1) to find the angle

tan^-1(tan(theta))=tan^-1(3)

theta=71.56

 

So the man would have to look at a 71.6degree angle above horizontal to see the top of the ladder.