Question

If the side opposite a 60-degree angle in a 30-60-90 right triangle is 73–√ cm 7 3 cm long, how long is the hypotenuse?(1 point) Responses 14 cm 14 cm 7√3 cm 7 3 cm 7 Start Root 3 End Root cm 28 cm 28 cm 7 cm

Answer 1

In a 30-60-90 triangle, the ratios of the sides are as follows:

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

You've indicated that the side opposite the 60-degree angle is \( 73 - \sqrt{cm} \) (I'll assume you meant 73 cm). We can set up our equation based on the properties of a 30-60-90 triangle.

Given:
- Side opposite the 60-degree angle = \( x\sqrt{3} \)
- \( x\sqrt{3} = 73 \)

To find the length of the hypotenuse:
1. Solve for \( x \):
\[
x = \frac{73}{\sqrt{3}}
\]

2. The hypotenuse is:
\[
2x = 2 \cdot \frac{73}{\sqrt{3}} = \frac{146}{\sqrt{3}} \approx 84.55 cm
\]

However, if you meant that the exact length of the side opposite the 60-degree angle is \( 7\sqrt{3} \):

1. Then:
\[
x\sqrt{3} = 7\sqrt{3}
\]
Here, \( x = 7 \).

2. The hypotenuse is:
\[
2x = 2 \cdot 7 = 14 \, \text{cm}
\]

So, the hypotenuse would be **14 cm**.