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

Answer:

$c = 2\sqrt{5$

Step-by-step 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

$c = \sqrt{4} * \sqrt{5$

Take square root of 4

$c = 2 * \sqrt{5$

$c = 2\sqrt{5$