Question

In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?

Answer 1

Knowing the sine of angle A, you can easily determine the angle A. You can do this using your trig circle or table, or computing sine-inverse. But in any case, you'll get A=30-degrees. Using the fact that a triangle's interior angles sum to 180, you can determine the remaining angle must be 60-degrees, so this is a 30-60-90 triangle. Since BC is the leg adjacent to the 60-degree angle, we regard it as x in the 30-60-90 ratio, and AC is the hypotenuse. Therefore, since the hypotenuse is always twice as long as this leg, the hypotenuse is length 16 inches.