Question

Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. $$a=5, c=13$$

Short answer

The missing length (b) of the right triangle is 12.

Step-by-step solution

Identify the Given Values

In the problem, we are given the values of a and c. Specifically, \(a = 5\) and \(c = 13\). We are required to find the length of b

Apply Pythagoras' Theorem

The formula that we will use is derived from the Pythagorean theorem and is \(b = \sqrt{c^{2} - a^{2}}\). Substituting \(a = 5\) and \(c = 13\) we get \(b = \sqrt{(13^{2}) - (5^{2})}\).

Calculate the Result

Carry out the operation in the brackets first: \(b = \sqrt{(169) - (25)} = \sqrt{144}\). Find the square root of 144 to find the length of b. So, \(b = 12\).