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.AnswersThe side opposite the second triangle’s 25° angle has length 4.The side opposite the second triangle’s 25° angle has length $8\sqrt{21}$.The side opposite the second triangle’s 25° angle has length 64.The side opposite the second triangle’s 25° angle has length 8.

Answer 1

Because both right triangles have the same acute angle (25°), they are similar. The scale factor from the first triangle (hypotenuse 40) to the second (hypotenuse 10) is 10/40 = 1/4. So the opposite side scales the same: 16·(1/4) = 4.

Answer: 4.