1)
a) Use pythagorean theorem: x = 15
b) sin A = 9/15 = 3/5
cos B = 9/15 = 3/5
They are equal because sine and cosine are cofunctions.
c) Since sin A = 3/5
We can figure out A by figuring out sin^-1 (3/5)
Using a calculator A ≈ 36.87 degrees
2) Inverse trig functions are used to figure out the measure of the angles. For example to find out the angle measure B, we can use:
sin^-1 (12/15) ≈53.13 degrees
3) tan 43 = x/16
x = 16 tan 43
x ≈ 14.92