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

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 64.

Answer 1

Because the triangles are similar (same angle 25°), the ratio opposite/hypotenuse is constant: 16/40 = 0.4. For the second triangle opposite = 0.4·10 = 4.

Answer: 4.