Question

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
7 cm
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Answer 1

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

- 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 \(2x\).

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 \(\sqrt{3}\):

\[
x = 7 \, \text{cm}
\]

Now, we can calculate the hypotenuse:

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

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