Question

HELP PLS! Worth 20 points!!

What is the hypotenuse and the shorter leg of a 30-60-90 triangle, if the longer leg is 12?

Answer 1

Let the hypotenuse be y and the shorter leg be x
sin30°= SHORTER LEG/HYPOTENUSE
1/2=x/y
2x=y..........(1)

cos30°=LONGER LEG/HYPOTENUSE
Root3/2=12/y
y=8 Root 3 units

Substituting y in equation 1:
2x=8 Root 3
x= 4 Root 3 units

Thus, the value of the hypotenuse is 8 Root 3 units, and the value of the shorter leg is 4 Root 3 units.