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By Cynthia Y Young

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2, we reviewed the fact that triangles with equal corresponding angles also have proportional sides and are called similar triangles. The concept of similar triangles (one of the basic insights in trigonometry) allows us to determine the length of a side of one triangle if we know the length of one side of that triangle and the length of certain sides of a similar triangle. Since the two right triangles to the right have equal angles, they are similar triangles, and the following ratios hold true: c a b c a ϭ ϭ ar br cr b WORDS Start with the first ratio.

In Exercises 79–82, use the figure below: 81. If AC ϭ 30, AB ϭ 24, and DC ϭ 11, find AD. 82. If AB ϭ 60, AD ϭ 61, and DC ϭ 36, find AC. 83. Given a square with side length x, draw the two diagonals. The result is 4 special triangles. Describe these triangles. What are the angle measures? 84. Solve for x in the triangle below. A 2x + 2 3x – 2 B D C 79. If AB ϭ 3, AD ϭ 5, and AC ϭ 158, find DC. x 80. If AB ϭ 4, AD ϭ 5, and AC ϭ 141, find DC. ■ T E C H N O L O G Y 85. 68 feet, what are the lengths of the other leg and the hypotenuse?

Sec u 5. tan u 6. 3 Definition 1 of Trigonometric Functions: Right Triangle Ratios 35 In Exercises 7–12, refer to the triangle in the drawing to find the indicated trigonometric function values. Rationalize any denominators containing radicals that you encounter in the answers. 7. cos u 8. sin u 9. sec u 10. csc u 11. tan u 12. cot u 2 ␪ 1 In Exercises 13–18, refer to the triangle in the drawing to find the indicated trigonometric function values. Rationalize any denominators containing radicals that you encounter in the answers.

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