Explanation:
The most important thing to remember is: SOH CAH TOA
sin(x) = opposite/hypotenuse
cos(x) = adjacent/hypotenuse
tan(x) = opposite/adjacent
So in #1:
We have the angle and hypotenuse and need to solve for the side opposite of the angle. This smells like a sine question.
sin(42)=x/25
this means that x=25sin(42). Plug that into the calculator and get: 16.73.
(Make sure you are in degrees mode)
For #2:
We are given the angle, the opposite side, and have to solve for the adjacent side. Looks like we need the tangent.
tan(75)=12/x
This means that x=12/tan(75). Calculator says: 3.22
For #3:
We have the angle, adjacent, and have to solve for the hypotenuse. This would be a cosine.
cos(36)=19/x
Solve for x: x=19/cos(36). Calculator says: 23.49
For #4:
We have the angle, adjacent side, and need the opposite side. This is another tangent problem.
tan(53)= x/7
Solving for x: x=7tan(53). Calculator says: 9.29