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12-63.

A -- triangle has a hypotenuse of length units. Sketch and label the triangle, including the length of each side. Then use your diagram to determine exact values for the following trig expressions.

Right triangle labeled as follows: horizontal leg, x times the square root of 3, vertical leg, x, hypotenuse, 2, x, angle opposite horizontal leg, 60 degrees, angle opposite vertical leg, 30 degrees.

  1. How is related to ? Is the relationship true for any pair of acute angles in a right triangle? Explain your reasoning.

Compute without a calculator