How do you find the remaining side of a #30^circ-60^circ-90^circ# triangle if the longest side is 8?

1 Answer
Jan 4, 2018

The three sides are 4, #4sqrt(3)#, and 8.

Explanation:

The ratio of the sides in a 30-60-90 triangle is #x:xsqrt(3):2x#. That means if the side opposite #30^circ# is #x#, then the side opposite #60^circ# is #xsqrt(3)# and the side opposite #90^circ# is #2x#.

Since the longest side is the hypotenuse, which is opposite #90^circ#, we know that #2x = 8\rightarrow x = 4#. So the side opposite #30^circ# is 4.

If the side opposite #30^circ# is 4, we know that the side opposite #60^circ#, #xsqrt(3)#, is going to be #4sqrt(3)#.

So the sides are 4, #4sqrt(3)#, and 8.