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In the last lesson we used the Law of Cosines to find the length of the third side of a triangle when you know the length of two sides and the angle in between. This law can also be used to find the measure of an angle when the three sides of a triangle are given. To use the Law of Cosines to find an unknown angle: 1. Identify c as the side across from the angle you are trying to find. 2. Substitute the values into the Law of Cosines.
Since we know the 53 angle, the hypotenuse ,and we want to find length of the opposite side, we should use sine. Step 2. Set up an equation based on the ratio you chose in the step 1. $ sin(53) = \frac{opposite}{hypotenuse} \\ sin(53) = \frac{x}{15} $. Step 3. Cross multiply and solve the equation for the side length.irections: Use sohcahtoa to find the given side length. Based on your givens and unknowns, determine which sohcahtoa ratio to use. Since we know the 67 angle, its adjacent side length and we want to know length of the opposite side, we should use tangent. Set up an equation based on the ratio you chose in the step 1.