Question

A 50-foot ladder leans against a wall 15 feet from the base of the wall. What is the measure of the angle formed by the ladder and the wall? Please show all work.

Answer 1

Answer:

72.5°

Step-by-step explanation:

This is a right triangle problem.  The ladder is the hypotenuse, and we have a length for that of 50 feet.  We also have the distance along the ground that the ladder's base is from the wall against which it is leaning.  This is the side adjacent to the angle for which we are seeking, so it the side adjacent to the angle, and it measures 15 feet.

We need a trig ratio that relates the side adjacent to the hypotenuse.  That will be the cosine.  Setting up:

$cos\theta =\frac{adjacent}{hypotenuse}$ and then filling in:

$cos\theta=\frac{15}{50}$

Use the 2nd button on your calculator, and then press cos and you will get a display on your screen that looks like this:

$cos^{-1}($

After that open parenthesis enter the fraction 15/50 and hit enter and you'll get the angle of 72.5 degrees, rounded.

Answer 2

just an addition to that superb reply above by @Luv2Teach

to the risk of sounding redundant.

Check the picture below.

make sure your calculator is in Degree mode.