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Name: ___________________________________ Date: 3/19/2014 Standard: Trigonometric Ratios Mr. Murpheyβs Analytical Geometry Block: 2 SWABAT Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle (MCC912. G.SRT.6) Inbox Task Write each fraction as a decimal rounded to the nearest hundredth. 1. π 2. π π ππ Simplify each expression. π π.π 4. . ππ = π.π 3. . π = π Trigonometric Ratios In Exercises 1β3, fill in the blanks to complete each definition. Then use side lengths from the figure to complete the indicated trigonometric ratios. 1. The sine (sin) of an angle is the ratio of the length of the leg _____________________ the angle to the length of the _____________________. sin A ο½ c sin B ο½ 2. The cosine (cos) of an angle is the ratio of the length of the leg _____________________ to the angle to the length of the _____________________. cos A ο½ c cos B ο½ 3. The tangent (tan) of an angle is the ratio of the length of the leg _____________________ the angle to the length of the leg _____________________ to the angle. a tan B ο½ tan A ο½ Use the figure for Exercises 4β6. Write each trigonometric ratio as a simplified fraction and as a decimal rounded to the nearest hundredth. 4. sin L 5. cos L ________________________ ________________________ 6. tan M _________________________ Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. 7. sin 33ο° 8. cos 47ο° 9. tan 81ο° ________________________ ________________________ _________________________ Use a calculator and trigonometric ratios to find each length. Round to the nearest hundredth. 10. 11. 12. BD ________________ QP _________________ RS _________________ 13. The glide slope is the path a plane uses while it is landing on a runway. The glide slope usually makes a 3ο° angle with the ground. A plane is on the glide slope and is 1 mile (5280 feet) from touchdown. Use the tangent ratio and a calculator to find EF, the planeβs altitude, to the nearest foot. Use the figure for Exercises 1β6. Write each trigonometric ratio as a simplified fraction and as a decimal rounded to the nearest hundredth. 1. sin A 2. cos B ________________________ 4. sin B ____________________ 3. tan B ________________________ 5. cos A ________________________ _________________________ 6. tan A ________________________ _________________________ Use special right triangles to write each trigonometric ratio as a simplified fraction. 7. sin 30ο° ________ 8. cos 30ο° ________ 9. tan 45ο° ________ 10.tan 30ο° ________ 11. cos 45ο° ________ 12. tan 60ο° ________ Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. 13. sin 64° ________ 14. cos 58° ________ 15. tan 15° ________ Find each length. Round to the nearest hundredth. 16. 17. XZ _____________ 19. 18. HI _____________ 20. ST _____________ KM _____________ 21. EF _____________ 21.A ramp is used to load a 4-wheeler onto a truck bed that is 3 feet above the ground. The angle that the ramp makes with the ground is 32°. What is the horizontal distance covered by the ramp? Round to the nearest hundredth. DE _____________ 22. A right triangle has an angle that measures 55°. The leg adjacent to this angle has a length of 43 cm. What is the length of the other leg of the triangle? Round to the nearest tenth.