Question

If the side opposite a 60-degree angle in a 30-60-90 right triangle is 7√3 cm
long, how long is the hypotenuse?(1 point)
Responses

28 cm
28 cm

14 cm
14 cm

7√ 3cm
7 Start Root 3 End Root cm

7 cm

Answer 1

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

- The side opposite the 30-degree angle (the shortest side) is denoted as \(x\).
- The side opposite the 60-degree angle is \(x\sqrt{3}\).
- The hypotenuse (opposite the 90-degree angle) is \(2x\).

Given that the side opposite the 60-degree angle is \(7\sqrt{3}\) cm, we set up the equation:

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

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

\[ x = 7 \]

Now, we find the hypotenuse:

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

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