Question

Find the missing side lengths. Leave your answers as radicals in simplest form. Show your work to support your answer ​

Answer 1

Answer

x=2 and y=2√2

Step-by-step explanation:

$\sin( \alpha ) = \frac{2 \sqrt{2} }{x } \\ x = \frac{2 \sqrt{2} }{ \sin(45) } \\ x = 4 \\ {x}^{2} = {y}^{2} + 2 \sqrt{2} \\ {4}^{2} = {y}^{2} + (2 \sqrt{2 \: )}^{2} \\ 16 = {y}^{2} + 8 \\ 16 - 8 = {y}^{2} \\ y = \sqrt{8} \\ y = 2 \sqrt{2}$