Question

What is the length of the side opposite to a 30 degree angle if it is 12 units less than the hypotenuse of the triangle?

Answer 1

30-60-90 special triangle has sides in the ratio of

1 : sqrt 3 : 2 (a:b:c)

sin A = a/c = 1/2
hypotenuse = c = h
side a = h - 12 (opposite 30 deg angle)

set-up a ratio
1/2 = (h - 12)/h
cross multiply
h = 2(h - 12)
h = 2h - 24
-h = -24
h = 24

hypotenuse = 24
side a (opposite 30 d angle)= h - 12
side a = 24 - 12
side a = 12

length of side = 12 units