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Original Question
A right triangle has a hypotenuse of length 40 and an angle of 25°, with a side opposite this angle of length 16. A second righ...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 12√3
.
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.
The side opposite the second triangle’s 30° angle has length 3.
The side opposite the second triangle’s 30° angle has length 6.
Responses
The side opposite the second triangle’s 30° angle has length 12√3
.
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.
The side opposite the second triangle’s 30° angle has length 3.
The side opposite the second triangle’s 30° angle has length 6.
Answers
GPT-4o mini
In a right triangle with an angle of 30°, the side lengths follow a specific ratio. Specifically, the side opposite the 30° angle is half the length of the hypotenuse.
For the second triangle, we have a hypotenuse of 12. To find the length of the side opposite the 30° angle, we can use the relationship mentioned:
\[
\text{Length of the side opposite 30°} = \frac{1}{2} \times \text{Hypotenuse} = \frac{1}{2} \times 12 = 6.
\]
Thus, the length of the side opposite the 30° angle in the second triangle is **6**.
For the second triangle, we have a hypotenuse of 12. To find the length of the side opposite the 30° angle, we can use the relationship mentioned:
\[
\text{Length of the side opposite 30°} = \frac{1}{2} \times \text{Hypotenuse} = \frac{1}{2} \times 12 = 6.
\]
Thus, the length of the side opposite the 30° angle in the second triangle is **6**.