Question

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

Answer 1

a = 3√2;

b = 3

Explanation:

Use trigonometry:

`\tan(45°) = (b)/(3)`

Cross-multiply to find b:

`b = 3 * \tan(45°) = 3 * 1 = 3`

Use the Pythagorean theorem to find a:

`{a}^(2) = {3}^(2) + {b}^(2)`

`{a}^(2) = {3}^(2) + {3}^(2) = 9 + 9 = 18`

`a > 0`

`a = √(18) = √(9 * 2) = 3 √(2)`