Question

angle S=90 degree, angle P=30 degree, side SR=6, triangle PSR is a right angled triangle. find RP & SP

Answer 1

Given: angle S=90 degree, angle P=30 degree, side SR = 6 units

To find: RP & SP

Solution:

• Now we have given that angle S=90 degree, angle P=30 degree the angle R will be:

                      P + S + R = 180

                      R = 180 - (90 + 30)

                      R = 180 - 120

                      R = 60 degree.

• Now in triangle PRS, let SP be base, SR be perpendicular and PR be hypotenuse, so :

                      sin 30 = perpendicular / hypotenuse

                      1/2 = 6 / hypotenuse

                      hypotenuse = 12 units.

• Similarly:

                      cos 30 = base / hypotenuse

                      √3 / 2 = base / 12

                      base = 6√3 units.

Answer:

               So the length if SP is 6√3 units and PR is 12 units.