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)

Question

Responses

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.

The side opposite the second triangle’s 30° angle has length 123–√
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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 6.

Answer 1

In a right triangle with an angle of 30°, the side opposite the 30° angle is half the length of the hypotenuse.

In the second triangle you described, the hypotenuse is 12. Therefore, the length of the side opposite the 30° angle can be calculated as follows:

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

Thus, the length of the side opposite the second triangle's 30° angle is 6.