One of the acute angles of a right triangle is 50 ° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.

In a right triangle:

the sine of an angle * length (the hypotenuse) = length (opposite leg)

the cosine of that angle * length (the hypotenuse) = length (adjacent leg)

Using a scientific calculator we find: sin50°=0.766; cos50° = 0.643

thus, the legs are:

|opp leg| = sin50° * 7 in = 0.766 * 7 in = 5.4 in

|adj leg| = cos50° * 7 in = 0.643 * 7 in = 4.5 in

Answer:

5.4, 4.5