Find the missing side of the right triangle

Question

8in 13in

a) 5 in     b) 105 in     c) √105 in     d) √233 in

Answer 1

The key to this problem is that we know, thanks to the question, that this is a right triangle! The side lengths of right triangles can always be found using the Pythagorean Theorem: a² + b² = c² .

This problem gives us side-length a as 8 units, and side-length c as 13 units. We solve by plugging them into the Pythagorean Theorem, like so: 8² + b² = 13² ; we solve by subtracting 8² from both sides, getting b² = 13² - 8². Now, all we have to do is solve! The math for b² works out to 13² - 8² = 169 - 64 = 105 = b² ; to get b we just take the square root of both sides, and get our final answer as √105!

Answer 2

x^2=13^2 - 8^2 = 105

x = √105