Question

Find the missing side lengths. Leave your answers as radicals in simplest form

Answer 1

a = b = 3√2

Explanation:

Use trigonometry:

`\sin(45°) = (a)/(6)`

Cross-multiply to find a:

`a = 6 * \sin(45°) = 6 * ( √(2) )/(2) = (6 √(2) )/(2) = 3 √(2)`

Use the Pythagorean theorem to find b:

`{b}^(2) = {6}^(2) - {a}^(2)`

`{b}^(2) = {6}^(2) - ( {3 √(2)) }^(2) = 36 - 9 * 2 = 36 - 18 = 18`

`b > 0`

`b = √(18) = 3 √(2)`