Question

Find the missing length
. Leave your answers in simplest radical form

Answer 1

Use the Pythagorean theorem:

`x^2+8^2=16^2\\\\x^2+64=256\qquad\text{subtract 64 from both sides}\\\\x^2=192\to x=√(192)\\\\x=√(64\cdot3)\\\\x=√(64)\cdot\sqrt3\\\\\boxed{x=8\sqrt3\ in}`

`x^2+5^2=(√(122))^2\\\\x^2+25=122\qquad\text{subtract 25 from both sides}\\\\x^2=97\to \boxed{x=√(97)\ in}`