Question

In the 30-60-90 triangle below, side s has a length of _____ and side q has a length of _____.

Answer 1

In a 30-60-90 triangle, the rule is:

If opposite of 30° is x,
1) Opposite of 60° is x√3
2) Opposite of 90° is 2x

When we put that into consideration, they gave us the opposite of 90° which is 8. If 8 is 2x, x or opposite of 30° is 4.

For q, we need to multiply s by √3: $4 \times \sqrt{3} = 4 \sqrt{3}$

So, q is 4√3.

Answer 2

In a 30-60-90 triangle, the side lengths are in the ratio 1:2:sqrt(3) = short leg: hypotenuse: long leg.

We know the hypotenuse is 8. We can use this to find the other legs.

The short leg s is 8/2 = 4 because the short leg is always half of the hypotenuse.

The long leg q is 4 * sqrt(3), because the long leg is always sqrt(3) times the shorter leg.

So:

s = 4

q = 4 * sqrt(3)