Question

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.

Answer 1

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