Question

Help please !!!! i’ll give brainliest .

Answer 1

Answer:

x=9$\sqrt{2}$ 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 $x\sqrt{3}$, and the hypotenuse (opposed to 90-degree angle) is 2x.

Solve:

the hypotenuse right here is $6\sqrt{3}$ and the rule for hypotenuse is 2x. set equation 2x=$6\sqrt{3}$ and solve for x. x=$3\sqrt{3}$. 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 ($x\sqrt{3}$). plug $3\sqrt{3}$ that we solved before to $x\sqrt{3}$, so ($3\sqrt{3}$)($\sqrt{3}$). 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 $\sqrt{2}$ 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)($\sqrt{2}$) and get your x, the hypotenuse. x=9$\sqrt{2}$