4. What you want to do is first find the tan ratio, because tangent is opposite / adjacent, which you can use to find x.
So tan(52) = 1.28 ish. So we know that x/18 = 1.28.
Then multiply both sides by 18.
x / 18 * 18 = 1.28 * 18
x = about 23.
5. Now, you can use the pythagorean's theorem, a^2 + b^2 = c^2.
Just input all values.
18 ^ 2 + 23 ^ 2 = c ^ 2
324 + 529 = c ^ 2
853 = c^2
square root of 853 = c
x = 29.2 ish
6. In this case, use cosine, or adjacent / hypotenuse.
cos(16) = 0.96 ish
so that means 24/x = 0.96
Then basically,
24 / 0.96 = x
x = 25
So x = 25
Then you can use the Pythagorean's Theorem again. I'm not going to go as in depth.
a ^ 2 + b ^ 2 = c ^ 2
24 ^ 2 + b ^ 2 = 25 ^ 2
576 + b ^ 2 = 625
b ^ 2 = 49
b = 7
8. Use tan here. opposite/adjacent Again, not going as in depth.
tan(55) = 1.43 ish
1.43 = Y / 22
1.42 * 22 = Y
Y = 31.24 ish
Length of MN:
31.24 ^ 2 + 22 ^ 2 = c ^ 2
976ish + 484 = c ^ 2
1460 = c ^ 2
x = 38.2 ish
10. Use cosine.
cos(63) = about 0.45
Adjacent / hypotenuse
3 / x = 0.45
3 / 0.45= x
x = 6.67
And then pythagorean's Theorem.
6.67 ^ 2 = 3 ^ 2 + b ^ 2
44.5 = 9 + b ^ 2
35.5 = b^2
b = about 6
