Question

Luke wants to install a string of lights along the roof of his house, and he needs to confirm that the total length of his roof is 100 feet. The roof is formed by two back-to-back right triangles, as pictured below. The base of the larger triangle is 7y feet in length and makes an angle of elevation of x degrees with the tip of the roof. The base of the smaller triangle is 3x feet in length and makes an angle of y degrees with the tip of the roof.

Answer 1

100 = 7y/cos x + 3x/cos y

Explanation:

In the picture attached, the question is completed.

The length of the lights is the addition of the 2 hypotenuses (h1 and h2).

cos x = 7y/h1

Isolating h1: h1 = 7y/cos x

cos y = 3x/h2

Isolating h2: h2 = 3x/cos y

Adding the lengths of the hypotenuses and substituting:

100 = h1 + h2

100 = 7y/cos x + 3x/cos y