Can you let me know if I got these right please? I need to find the remaining sides of these triangles.?

Question

If you are visual, there are three right triangles, each with at least one variable. I'm supposed to find those variables.

I will start at the BOTTOM LEFT CORNER where the right triangle is, move up (giving the length of that line), then down the hypotenuse (giving the length), and across the bottom line, doing the same thing.

The angle given is between the hypotenuse and adjacent line (although the third triangle has no angle)

Please help!

1. Triangle 1 (45 Degrees):

Side 1: A

Side 2: 3 root(2)

Side 3: B

-------

Triangle 2 (30 Degrees):

Side 1: 5

Side 2 (H): C

Side 3: B


---------------

Triangle 3:

Side 1: 5

Side 2: 13

Side 3: B

Answer 1

TRIANGLE 1:

A and B are equal in a 45 degree triangle.

A² + B² = C²
A² + B² = (3√2)²
A² + A² = 18
2A² = 18
A² = 9
A = 3
B = 3

TRIANGLE 2:
The ratio of sides in a 30-60-90 triangle are 1:2:√3 It's unclear if 5 is your shorter leg, but I'll assume so.

C = 2A = 2(5) = 10

A² + B² = C²
5² + B² = 10²
25 + B² = 100
B² = 100 - 25
B² = 75
B = √75
B = 5√3

TRIANGLE 3:

A² + B² = C²
5² + B² = 13²
25 + B² = 169
B² = 169 - 25
B² = 144
B = √144
B = 12