Answer:
x=9[tex]\sqrt{2}[/tex] and y=9
Step-by-step explanation:
solve for the 60 degree triangle first. so we know the sum of the angles in a triangle is 180 degrees. then .
Rule for 30 60 90 triangle:
180-60-90=30 for the triangle on the right. use the rule for 30 60 90 triangle, which is the shortest side (opposed to 30-degree angle) is x, the second-longest side (opposed to 60-degree angle) is [tex]x\sqrt{3}[/tex], and the hypotenuse (opposed to 90-degree angle) is 2x.
Solve:
the hypotenuse right here is [tex]6\sqrt{3}[/tex] and the rule for hypotenuse is 2x. set equation 2x=[tex]6\sqrt{3}[/tex] and solve for x. x=[tex]3\sqrt{3}[/tex]. this is only the answer for the shortest side of the triangle on the right.
now solve for y on your picture. look at the rule for the second-longest side ([tex]x\sqrt{3}[/tex]). plug [tex]3\sqrt{3}[/tex] that we solved before to [tex]x\sqrt{3}[/tex], so ([tex]3\sqrt{3}[/tex])([tex]\sqrt{3}[/tex]). you get y=9.
Rule for 45 45 90 triangle:
180-45-90=45 for the triangle on the left. Use the rule for 45 45 90 triangle, which is the length of the hypotenuse is [tex]\sqrt{2}[/tex] times the length of a leg, and the two legs have the same length.
Solve:
On the picture, the y is one of the legs. So now (9)([tex]\sqrt{2}[/tex]) and get your x, the hypotenuse. x=9[tex]\sqrt{2}[/tex]