Question

If the side opposite a 60-degree angle in a 30-60-90- right triangle is 7 square root of 3 cm long, how long is the hypotenuse?

a. 14 cm
b. 7 cm
c. 7 square root 3 cm
d. 28 cm

Answer 1

In a 30-60-90 triangle, the lengths of the sides are in the ratio of 1 : √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 side opposite the 60-degree angle is \( 7\sqrt{3} \) cm, we can set up the equation:

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

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

\[
x = 7
\]

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

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

Therefore, the length of the hypotenuse is \( \boxed{14} \) cm.