Question

Find the missing side of the triangle. Side LaTeX: cc is the hypotenuse and sides LaTeX: aa and LaTeX: bb are legs. Leave your answer in simplest radical form. LaTeX: a=2,\:b=4

Answer 1

`c = 2\sqrt{5`

Explanation:

Given

`a = 2`

`b = 4`

c = hypotenuse

Required

Find c

Using Pythagoras theorem, we have:

`c^2 = a^2 + b^2`

Substitute values for a and b

`c^2 = 2^2 + 4^2`

`c^2 = 4 + 16`

`c^2 = 20`

Take square roots of both sides:

`c = \sqrt{20`

Express 20 as 4 * 5

`c = \sqrt{4 * 5`

Split surd

`c = √(4) * \sqrt{5`

Take square root of 4

`c = 2 * \sqrt{5`

`c = 2\sqrt{5`