Question

Find x on this special right triangle, 45 is not an option!!!!

Answer 1

let the line between 2 tria be y

sin 60/8√2 = sin 90/y

y=13.06

sin 45/13.06 = sin 90/x

x=18.46

Answer 2

First, find the hypotenuse of the right triangle with the 60° & 30°.

• Hypotenuse = h
• sin(x) = opposite side/hypotenuse

`sin(60) = (8√(2))/(h) \\\\sin(60)h=8√(2)\\\\(√(3))/(2) h=8√(2)\\\\h=(8√(2))/((√(3))/(2))=8√(2)*(2)/(√(3)) =(16√(2) )/(√(3)) =(16√(2)(√(3)) )/(√(3)(√(3))) =(16√(6) )/(3)`

Use that side length to find x.

• sin(x) = opposite side/hypotenuse

`sin(45)=((16√(6))/(3))/(x)\\\\sin(45)x=(16√(6))/(3) \\\\(√(2))/(2)x=(16√(6))/(3) \\\\x=((16√(6))/(3))/((√(2))/(2))=(16√(6))/(3)*(2)/(√(2))=(16√(2)√(3)(2))/(3√(2) )=(32√(3) )/(3)`