Question

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

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−−√
.

Answer 1

Use similarity (same acute angle => triangles are similar). Opposite/hypotenuse stays proportional:
16/40 = x/10, so x = 10*(16/40) = 4.

Answer: 4.