Answer:
Step-by-step explanation:
You want the legs of a 30°-60°-90° triangle with hypotenuse 15 in.
A 30°-60°-90° triangle is one of two "special" right triangles often seen in trig and geometry problems. As you know, the ratio of side lengths in this triangle is ...
1 : √3 : 2
Multiplying these ratio values by 7.5, we find the lengths of the sides of the given triangle to be ...
7.5 : 7.5√3 : 15
The legs have lengths 7.5 inches and 7.5√3 ≈ 12.99 inches.
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Additional comment
The other special triangle is the isosceles right triangle, 45°-45°-90°. Its sides have the ratio 1 : 1 : √2.
If you haven't learned these triangles yet, you can figure the lengths using the trig relations:
short side = hypotenuse × sin(30°) = 15×1/2 = 7.5 . . . inches
longer side = hypotenuse × cos(30°) = 15×(√3)/2 = 7.5√3 . . . inches.