Question

A board with a length of 15 feet is leaning against a vertical wall at a point that is 12 feet above the ground. The angle that the board forms with the ground is 53.13°. Use a trigonometric function to determine the distance from the bottom of the board to the edge of the wall. In at least four sentences, explain why you chose your specific function and how it applies to the reference angle A. Be sure to include the key vocabulary words "sine", "ratio", "opposite side", "hypotenuse" and "angle measure" in your response. Describe each computational step in complete sentences.

Answer 1

In fact, the AB could be calculated in a quickest way, using Pythagorean theorem. In here, we try to use the property of trigonometry to work out AB.

Before applying trigonometry, in this right triangle we can calculate the remaining angle C:

C = 180 - 90 - A = 180 - 90 - 53.13 = 36.87 deg

We can use cosine formula, but here we use the sine formula for the sake of convenience. We have:

sine(angle measure) = ratio of opposite side over hypotenuse

In detail, sineC = AB/BC

Then, we have: AB = BC x sineC = 15 x sin(36.87 deg) = 9.000002 = ~9 ft

Hope this helps!

:)