Question

The legs of a right triangle measure 5 inches and 7 inches. If theta is the angle between the 7 inch leg and the hypotenuse, sin theta = ___

Answer 1

sin (θ) = 0,58

Explanation:

The formula for sin (θ) is:

sin (θ) = (opposite side)/hypotenuse

The opposite side to the θ angle is the one that measures 5 inches, but we don’t know the measure of the hypotenuse. The Pythagoras theorem gives us the following formula:

side 1²+ side 2²= hypotenuse²

Then,

5²+7²=74

√74= 8,60 inches; this is the measure for the hypotenuse.

Replacing this value in the formula for sine:

sin (θ) = 5/8,60 = 0,58