Answer:
See below.
Explanation:
Some of your pictures are missing information, which angle is the right angle, but I will assume the information that is missing and will correct the incorrect information and will try to answer.
We are dealing with 30-60-90 and 45-45-90 triangles, so let's recall the ratios of the lengths of the sides of these two special right triangles.
The side lengths are listed in the following order in the ratios below:
30-60-90 triangle
short leg : long leg : hypotenuse
1 : √3 : 2
45-45-90 triangle
leg : leg : hypotenuse
1 : 1 : √2
1. Assume top angle is a right angle.
Upper triangle is a 30-60-90 triangle.
9√3 is opposite the 60° angle, so it is the longest side corresponding to 2 in the ratio.
x = (9√3)/√3 = 9
y = 2 × 9 = 18
Bottom triangle is a 45-45-90 triangle.
y = 18
z = 18/√2 = (18√2)/2 = 9√2
2.
Assume bottom left angle is a right angle.
Since 2 sides are congruent, they must be the legs.
This is a 45-45-90 triangle.
x = 7√2
3.
Assume bottom angle is right angle.
Short leg x
Long leg 9√3
This is the same triangle as the upper triangle of problem 1.
x = (9√3)/√3 = 9
y = 2 × 9 = 18
4.
The legs form the right angle and are congruent.
This is a 45-45-90 triangle.
x = 12/√2 = (12√2)/2 = 6√2
5.
I assume you mean the angle measure is 30° and not 130°.
Both triangles are 30-60-90 triangles.
Short leg: x
Long leg: 10
Hypotenuse: y
x = 10/√3 = (10√3)/3
y = 2 × (10√3)/3 = (20√3)/3
6.
30-60-90 triangle
short leg: 5√3
long leg: y
hypotenuse: x
x = 2 × 5√3 = 10√3
y = 5√3 × √3 = 15