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________________________loves the OLD HIPPIE Math II Unit 2 Test Period: ____________ Date: __________________ MM2G1 Students will identify and use special right triangles. MM2G1a Determine the lengths of sides of 30°-60°-90° triangles. MM2G1b Determine the lengths of sides of 45°-45°-90° triangles. Find the missing measures using special right triangles. Express answers in simplest radical form. Rationalize all denominators. 1. 2. 45 x 4 2 3. 4. y 5 60 6 x x 5. 6. x y 7 30 7 x 7. Find the diagonal of the rectangle: 12 30 A. 30 3 B. 24 3 C. 24 D. 12 3 E. None of the above 8. The length of a diagonal of a square is 20 inches. What is its perimeter? A. 50 in. these B. 40 2 in. C. 20 2 in. D. 30 2 in. E. None of 9.The side of an equilateral triangle is 18 meters. What is the height of the triangle? A. 9 m B. 20 2 m C. 9 2 m D. 9 3 m E. None of these 10. In a 30-60-90 right triangle, the length of the short leg is 5. Find the length of the hypotenuse. A. 3 5 B. 10 C. 5 2 D. 5 3 E. None of these MM2G2 Students will define and apply sine, cosine, and tangent ratios to right triangles. MM2G2a Discover the relationship of the trigonometric ratios for similar triangles. MM2G2b Explain the relationship between the trigonometric ratios of complementary angles. MM2G2c Solve application problems using the trigonometric ratios. 11. What is the sin, cos, and tangent of angle A? B (simplify) 20 16 C 12 A Solve for the missing measures using trig ratios. Show ALL work. Round to the nearest tenth. 12. 13. y 8 71 x 15 3 14. 3.7 15. 12 x x 17 6 16. In right ABC , A and B are the acute angles. If sin A = cos B = __? A. 257 these B. 24 25 C. 7 25 , what is D. Cannot be determined E. None of 7 24 17. A man that is 6 ft tall casts a shadow 14 ft long. Find the angle of elevation of the sun. 6 ft ??? 14 ft A. 66.8 B. 64.6 C. 23.2 D. 25.4 E. None of these Draw a diagram and solve the following. Round to the nearest tenth. Show ALL work. (Hint: Inverse trig functions) 18. A 16-foot ladder rests against a wall so that the base of the ladder is 6.5 feet from the base of the building. What angle does the ladder make with the ground? 19. In the diagram below, what is the measure of A to the nearest tenth of a degree? B A. 41.8 C. 33.7 B. 48.2 D. 1 8 A 12 C 20. The following two triangles are similar. What is sin A ? A B C 21.Find the height in feet of the Eiffel Tower if the angle of elevation from the base is 85.361 and the distance from the center to the outside of each leg is 80 feet. Bonus : Refer to the diagram. Find exact values of p, q, r, s, t, u, v and w. w 60 v 30 r u 45 s p q 3 t 30