Question

If the side opposite a 60-degree angle in a 30-60-90 right triangle is 7square root symbol3 cm long, how long is the hypotenuse?

Answer 1

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

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

In your case, the side opposite the 60-degree angle is given as \(7\sqrt{3}\) cm. According to the ratio:

\[
x\sqrt{3} = 7\sqrt{3}
\]

To find \(x\), divide both sides by \(\sqrt{3}\):

\[
x = 7
\]

Now we can find the hypotenuse, which is \(2x\):

\[
\text{Hypotenuse} = 2x = 2(7) = 14 \text{ cm}
\]

So, the length of the hypotenuse is \(14\) cm.