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step 1

so so s

Step-by-step 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