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 821−−√
.
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.
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.

Answer 1

The triangles are similar (same acute angle), so the opposite side scales with the hypotenuse by 10/40 = 1/4. Thus the opposite side = 16*(1/4) = 4.