Question

∠A is an acute angle in a right triangle.



Given that sin A=7/25, what is the ratio for cos A?



Enter your answer in the boxes as a fraction in simplest form

Answer 1

cos A = 24/25.

We know that the sine ratio is opposite/hypotenuse.  This gives us 2 of the sides of the right triangle; one leg is 7 and the hypotenuse is 25.  We can use the Pythagorean theorem to find the missing side:

7² + b² = 25²
49 + b² = 625

Subtract 49 from both sides:
49 + b² - 49 = 625 - 49
b² = 576

Take the square root of both sides:
√b² = √625
b = 24

Now that we have the adjacent side, we can find the cosine.  Cosine is adjacent/hypotenuse:
24/25