Math 11 Review Trigonometry
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1 Math 11 Review Trigonometry Short Answer 1. Determine the measure of D to the nearest tenth of a degree. 2. Determine the measure of D to the nearest tenth of a degree. 3. Determine the length of side z to the nearest tenth of a centimetre. 4. Determine the measure of V to the nearest tenth of a degree. 1
2 5. Determine the length of MN to the nearest tenth of an centimetre. 6. Determine the length of RS to the nearest tenth of a metre. 7. Determine the length of DE to the nearest tenth of a centimetre. 8. A road increases 8 m in altitude for every 100 m of horizontal distance. Calculate the angle of inclination of the road, to the nearest tenth of a degree. 9. A road rises 1 m for every 8.4 m measured along the road. What is the angle of inclination of the road to the nearest tenth of a degree? 10. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 22%. 11. A rope that anchors a hot air balloon to the ground is 136 m long. The balloon is 72 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a degree? 12. A wheelchair ramp is 7.0 m long. Its angle of inclination is 9. Calculate the rise of the ramp to the nearest tenth of a metre. 13. A guy wire is attached to a tower at a point that is 10 m above the ground. The wire is anchored 21 m from the base of the tower. What angle, to the nearest degree, does the guy wire make with the ground? 2
3 14. A helicopter is ascending vertically. On the ground, a searchlight is 125 m from the point where the helicopter lifted off the ground. It shines on the helicopter and the angle the beam makes with the ground is 48. How high is the helicopter at this point, to the nearest metre? 15. A flagpole casts a shadow that is 21 m long when the angle between the sun s rays and the ground is 48. Determine the height of the flagpole, to the nearest metre. 16. A student stood 8.0 m from the base of a tree. She used a clinometer to sight the top of the tree. The angle shown on the protractor scale was 65. The student held the clinometer 1.6 m above the ground. Determine the height of the tree to the nearest tenth of a metre. 17. A balloon is flying at the end of a 170-m length of string, which is anchored to the ground. The angle of inclination of the string is 50. Calculate the height of the balloon to the nearest metre. 18. The navigator of a ship at sea sees a lighthouse due north of the ship. The ship then sails 3.2 km due west. The angle between the ship s path and the line of sight to the lighthouse is How far is the ship from the lighthouse to the nearest tenth of a kilometre? 19. A water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. It then travels 15 km due east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the path it took due east and the path it will take to return directly to its dock? 20. The front of a tent has the shape of an isosceles triangle with equal sides 163 cm long. The measure of the angle at the peak of the tent is 105. Calculate the maximum headroom in the tent to the nearest centimetre. 21. Determine the area of RST to the nearest square centimetre. 3
4 22. Determine the length of RS to the nearest tenth of a centimetre. 23. Determine the measure of ABD to the nearest tenth of a degree. 24. Determine the length of QR to the nearest metre. 25. Calculate the measure of GHJ to the nearest tenth of a degree. 4
5 26. From the top of a 25-m lookout tower, a fire ranger observes one fire due east of the tower at an angle of depression of 7. She sees another fire due north of the tower at an angle of depression of 3. How far apart are the fires to the nearest metre? 27. A Girl Guide measured the angle of elevation of the top of a monument as 59. The height of the monument is 38.5 m. She then walked 31.0 m due west from the point where she measured the angle of elevation. Determine the angle of elevation of the monument from her new location to the nearest tenth of a degree. 5
6 ID: A Math 11 Review Trigonometry Answer Section SHORT ANSWER cm cm m cm m m m m m km cm cm cm m m 1
7 ID: A 27. Label a diagram. Use right ACD to calculate the length of CD. AD is opposite ACD and CD is adjacent to ACD. So, use the tangent ratio. tanc = opposite adjacent tanc = AD CD tan59 = 38.5 CD CD tan59 = 38.5 CD = 38.5 tan 59 CD = Use right ABD to calculate the measure of B. First determine the length of BD. BD = BC + CD BD = BD = Determine the measure of B. AD is opposite B and BD is adjacent to B. So, use the tangent ratio. tanb = opposite adjacent tanb = AD BD tanb = B = Τhe angle of elevation of the monument from the new location is approximately
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