Right triangles that contain common angles are triangles whose angles are 30°, 60°, and 90...

Right triangles that contain common angles are triangles whose angles are 30°, 60°, and 90° or triangles whose angles are 45°, 45°, and 90°. For each 30-60-90 triangle shown, you are given a, the side opposite the 30° angle.

a. Find the exact lengths of b, the side opposite the 60c angle, and c, the side opposite the 90° angle, for each triangle. Then fill in the table with these values.

b. If we let a represent the side opposite 30°, use the completed portion of the table to determine the pattern for the sides opposite the other angles in terms of a. Describe the pattern by completing the last row of the table for sides b and c in terms of a.

Then use your pattern to quickly find the remaining sides of the fol-lowing 30-60-90 triangle.