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. Two right triangles whose right angles are back-to-back. The measurements are labeled as described in the problem. The path of the lights goes along the outside of the roof, up one side to its peak, and then back down along the hypotenuses of the triangles.
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Which trigonometric equation correctly models the length of the roof in terms of x and y?