Question

Matt is painting the trim in his living room. He leans a ladder against the wall so that it forms an angle

elevation with the floor of 56°. If it is a 12-foot ladder, how high up on the wall does it reach? Round to
the nearest tenth.

Answer 1

9.9 inches

Explanation:

Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.

Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)

Therefore, we can now set up our equation and solve. (x is the height of the wall)

sin 56 =
`(x)/(12)` Initial equation

12 sin 56 = x Multiply each side by 12 so that we get x by itself.

x ≈ 9.9 Punch 12 sin 56 into a calculator and your done!

Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)