Question

In the right triangle shown, what is the cosine of angle C?

Answer 1

Answer:

A is correct

Step-by-step explanation:

Answer 2

Answer:

Since the legs of the right triangle measure x + 1 and x + 15, respectively, and since the hypotenuse measures x + 17, the Pythagorean Theorem can be used as follows: (x + 1)2 + (x + 15)2 = (x + 17)2. This equation becomes (x2 + 2x + 1) + (x2 + 30x + 225) = x2 + 34x + 289, which then becomes 2x2 + 32x + 226 = x2 + 34x + 289. When all the terms are moved to one side, the equation becomes x2 – 2x – 63 = 0, and when the left side of the equation is factored, it becomes (x – 9)(x + 7) = 0. At this point, it seems as if x can equal 9 or –7, but if x were –7, one of the legs would have a negative length, and this is impossible. For this reason x equals 9, and the legs of the triangle measure 10 and 24, respectively, while the hypotenuse measures 26. Since cosine is

length of adjacent leg

length of hypotenuse

, the cosine of angle C is

24

26

, or

12

13

.