Question

If the hypotenuse of a 30-60-90 triangle is 8 cm, how long is the side opposite the 60-degree angle?(1 point)

Answer 1

In a 30-60-90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\). This means:

- The side opposite the 30-degree angle is \(x\).
- The side opposite the 60-degree angle is \(x\sqrt{3}\).
- The hypotenuse is \(2x\).

Given that the hypotenuse is 8 cm, we can set up the equation:

\[
2x = 8
\]

Solving for \(x\):

\[
x = \frac{8}{2} = 4 \text{ cm}
\]

Now, to find the length of the side opposite the 60-degree angle, we use:

\[
\text{Side opposite 60 degrees} = x\sqrt{3} = 4\sqrt{3} \text{ cm}
\]

So, the length of the side opposite the 60-degree angle is \(4\sqrt{3}\) cm, which is approximately 6.93 cm if you need a decimal value.