1959 AMC 12 Problem 15

Attempt Problem 15 of the 1959 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1959 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

15.

In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:

15^\circ

30^\circ

45^\circ

60^\circ

75^\circ

Combine the given relation with the Pythagorean theorem

Compare

a^2+b^2

with

2ab

If the legs are

a,b

and the hypotenuse is

c,

then

a^2+b^2=c^2=2ab.

Hence

(a-b)^2=0,

so the legs are equal. The right triangle is isosceles and its acute angles are

45^\circ.

Thus, the correct answer is C.

Problem 15 in other years