If sin θ = 12 over 37, use the Pythagorean Identity to find cos θ.

We are asked to find and solve cos θ and the given os

sin θ = 12/37

By reviewing SOH CAH TOA, we will know that opposite measurement is equal to 12 units and the hypotenuse measurement is equal to 37 units. Since it is also mentioned in the problem that we can apply Pythagorean theorem, it means that the given is a right triangle. Then we can apply c ² = a² + b² formula.

Solving for adjacent side, we have:

37² = 12² + a²

a = 35

Solving for cos θ, we have CAH:

cos θ = 35/37

θ = 18.93 °