One
Since B and C are equal, you can with with C to get your answer.
In general the Cos(C) = adjacent / hypotenuse. Whatever you find out about C will apply to B.
The Cos of C = DC/AC
That is also the cos of B. Answer <<<<<
Two
This is a little bit nasty. Just go by the letters on the triangle. The small letters, not the capitals. b is the hypotenuse so whatever you answer, will not be the sine of anything or the cos of anything. That cuts out answers B, C and E
So a tangent = opposite divided by the adjacent. You want a/c
a is the opposite and c is the adjacent.
Tan (A) is the answer That's A.
Problem 3
The first thing I would do is to check to see that you are working with a right angle triangle. You probably are, but it will be quite nasty is not. The longest side is 22.5 so it have to be the hypotenuse.
a = 18
b = 13.6
c = 22.5
18^2 + 13.6^2 = ? 22.5^2
324 + 184.96 = 506.25 These are not equal, so you are not working with a right angle. You have 3 sides so you can use the cos law to find the two angles.
We'll find the angle opposite 18 first
b^2 = a^2 + c^2 - 2ac*cos(B)
18^2 = 22.5^2 + 13.6^2 - 2*22.5*13.6*Cos(B)
324 = 506.25 + 184.96 - 612*Cos(B)
324 = 691.21 - 612*cos(B)
324 - 691.21 = - 612*cos(B)
-367.21 = - 612*cos(B)
-367.21 / -612 = cos(B)
0.6 = cos(B)
B = cos-1(0.6)
B = 53.13 degrees. Round to whatever seems right.
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c = 13.6 so we are now looking for C.
I'm just going to outline what should be done. You can fill in the steps.
13.6^2 = 22.5^2 + 18^2 - 2*18*22.5*Cos(C)
184.96 = 506.25 + 324 - 810*cos(c)
184.96 = 830.25 - 810*cos(C)
-645.29 = - 810*cos(C)
0.7967 = cos(C)
C = cos-1(0.7967)
C = 37.18 degrees. I don't think I trust this. It looks too close to a right angle, but it is the answer I'm getting.
