Question

1 of 211 of 21 Items 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 length123–√ . The side opposite the second triangle’s 30° angle has length12 square root of 3. 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. The side opposite the second triangle’s 30° angle has length 3. Skip to navigation page 1 of 1

Answer 1

In a right triangle with an angle of 30°, the relationship between the lengths of the sides is significant. Specifically, in any right triangle:

- The side opposite the 30° angle is half the length of the hypotenuse.

For the second triangle, given that the hypotenuse is 12, we can determine the length of the side opposite the 30° angle by using this relationship:

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

Thus, the length of the side opposite the 30° angle in the second triangle is **6**.

So the corresponding response is:
**The side opposite the second triangle’s 30° angle has length 6.**