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Solve for in each of the following triangles. What methods can be used for finding unknown parts of triangles?

What laws and theorems relate the angles of a triangle to the sides? Or relate the lengths of the sides of a triangle to each other?
Use them to help you find the unknown parts of these triangles.

  1. Right triangle, labeled as follows: vertical leg, x, horizontal leg, 36, angle opposite horizontal leg, 24 degrees.

    Which trigonometric ratio relates the side opposite the angle to the side adjacent to it?

  1. Triangle, labeled as follows: right side, x, left side, 10, bottom left angle, 70 degrees, bottom right angle, 23 degrees.

    Remember that all the angles of a triangle add up to . Solve for the measure of the unknown angle. This will help you choose the correct law to solve for the unknown side.

    Use the Law of Sines.

  1. Triangle, labeled as follows: right side, 11, left side, 10, bottom side, 3, top angle, x.

    Use the Law of Cosines.