Question

If the side opposite a 60-degree angle in a 30-60-90 right triangle is
7V3 cm long, how long is the hypotenuse? (1 point)
O 7/3 cm
• 28 cm
• 7 ст
• 14 cm

Answer 1

In a 30-60-90 triangle, the ratios of the lengths of the sides are known. Specifically, the sides are in the ratio of 1 : √3 : 2. This means:

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

Given that the side opposite the 60-degree angle is \( 7\sqrt{3} \) cm, we can set this equal to \( a\sqrt{3} \):

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

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

\[
a = 7
\]

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

\[
\text{Hypotenuse} = 2a = 2 \times 7 = 14 \text{ cm}
\]

Therefore, the length of the hypotenuse is **14 cm**.