Question

A right triangle has a hypotenuse of length 24 and an angle of 30°, with a side opposite this angle of length 12. A second right triangle also has an angle of 30°, with a hypotenuse of length 12. Determine the length of the side opposite the 30° angle on the second triangle. (1 point)
Responses

The side opposite the second triangle’s 30° angle has length 6.
The side opposite the second triangle’s 30° angle has length 6.

The side opposite the second triangle’s 30° angle has length 123–√
.
The side opposite the second triangle’s 30° angle has length 12 Start Root 3 End Root .

The side opposite the second triangle’s 30° angle has length 24.
The side opposite the second triangle’s 30° angle has length 24.

The side opposite the second triangle’s 30° angle has length 3.

Answer 1

In a right triangle with a 30° angle, the lengths of the sides have a specific ratio. The side opposite the 30° angle is half the length of the hypotenuse.

For the second triangle, which has a hypotenuse of length 12, the length of the side opposite the 30° angle can be determined as follows:

\[
\text{Length of side opposite 30°} = \frac{1}{2} \times \text{Hypotenuse}
\]

Substituting in the value of the hypotenuse:

\[
\text{Length of side opposite 30°} = \frac{1}{2} \times 12 = 6
\]

Thus, the side opposite the second triangle’s 30° angle has length 6.

So the correct response is:

**The side opposite the second triangle’s 30° angle has length 6.**