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 right triangle also has an angle of 25°, with a hypotenuse of length 10. Determine the length of the side opposite the 25° angle on the second triangle.(1 point)
Responses

The side opposite the second triangle’s 25° angle has length 8.
The side opposite the second triangle’s 25° angle has length 8.

The side opposite the second triangle’s 25° angle has length 64.
The side opposite the second triangle’s 25° angle has length 64.

The side opposite the second triangle’s 25°angle has length 821−−√
8
21
.
The side opposite the second triangle’s 25°angle has length 8 Start Root 21 End Root .

The side opposite the second triangle’s 25° angle has length 4.

Answer 1

4

Since sin(25°) = opposite/hypotenuse = 16/40 = 0.4, for hypotenuse 10 the opposite side = 10·0.4 = 4 (or scale down by 10/40 = 1/4: 16·1/4 = 4).