The hypotenuse of a right triangle is 3 times as long as the shorter leg. Find the measure of the angle between the shorter leg and the hypotenuse.

Question

Its a word problem for applying inverse trigonometric functions.

Answer 1

Let Φ be the angle between the short leg and the hypotenuse

 

short leg = x ;  hypotenuse = 3x

 

Then cos Φ = x / 3x

 

         Φ =  cos ^-1 (1/3)

 

         Φ = 70.53°