Chapter 11 Applications in Trigonometry
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1 F.3 athematics Supplementary Worksheet for C 3 Chapter 11 ame: Class: 3 ( ) Date: Chapter 11 pplications in Trigonometry Level 1 1. eter walks up along an uphill road. The inclination of the road is 15. (a) What is the gradient of the road? (b) If eter walks 55 m, find his vertical rise. (8 marks) 2. The figure shows a contour map. straight road is constructed to connect and. If the gradient of the straight road is 1, find the actual 9 horizontal distance between and. 460 m 520 m 3. The figure shows two inclined planes and D. CD is a straight line. C D, DC = 14, D = 18 m and C = 12 m. Which inclined plane is steeper? 18 m 14 C D 12 m 4. In the figure, represents a platform of height 42 m. The angle of elevation of the top of the platform from a point on the ground is 34. is a point on the ground 42 m and is the mid-point of and. Find the angle of elevation of the top of the platform from the point. 34
2 5. Joe stands in front of a mountain and finds that the angles of elevation of the top and the bottom of a building on the mountain are 35 and 18 respectively. Given that the horizontal distance between the building and Joe is, what is the height of the building? 35 Joe In the figure, is a straight line. The angles of elevation of the top of the lighthouse from and are 35 and 21 respectively. If the height of the lighthouse is 15 m, find the distance between and m 7. In the figure,, and are the locations of three shopping malls. Find (a) the reduced bearing of from, (b) the whole circle bearing of from Starting from city S, lan drives 7 km due east. S 7 km Then he drives 10 km due south, and finally drives 4 km due west to reach city T. Find the reduced bearing of T from S. (Give the answer correct to the nearest degree.) T 4 km 10 km 9. The figure shows the positions of three ships, and C. is due north of, and C is at 38 E of. If C = 15 km and the bearing of from C is 55 W, find the distance between ships (a) and, (b) and C. 15 km C (14 marks)
3 Level 2 1. The figure shows a contour map of scale 1 : represents a straight road. Suppose the horizontal distance of is 1.5 cm on the map, find (a) the gradient of, express your answer in the 500 m 450 m 550 m form of 1, n (b) the angle that the road makes with the horizontal, correct to 3 significant figures. Scale 1 : The figure shows a map of scale 1 : straight road is going to be constructed to connect and. The horizontal distance of is 3.5 cm on the map. (a) Find the gradient of. Express your answer in the form of 1 : n, where n is correct to the nearest integer. (b) (i) Find the inclination of, correct to the nearest degree. (ii) Find the actual length of, correct to 3 significant figures. 600 m 500 m Scale 1 : (14 marks)
4 3. In the figure, a plane is 30 km above the ground. The angle of elevation of the plane from the top lane of a lighthouse of height 8 m is 40. Three minutes later, the plane is just above the lighthouse. What is the speed of its flight in km/h? 30 km 40 8 m 4. In the figure, is a straight line. is a lightning conductor of height 3 m. The angles of elevation of the top and the bottom of 3 m the lightning conductor from a point S are 38 and 31 respectively. Find the distance between and S S 5. The top of a building is observed from two positions and on the ground 60 m apart. The angles of elevation of from and are 45 and 60 respectively. Find the height of the building m 6. boat sails 3 km due west from pier. Then it sails 9 km due north, and finally sails 7 km due west to 7 km reach another pier. (a) Find the reduced bearing of from, correct 9 km to the nearest degree. (b) The boat sails back to pier along the straight line at a speed of 5 km/h. How many hours will it 3 km take to reach pier?
5 7. Two ships C and D left port O at 1 : 00 pm. Ship C sailed at a speed of 12 km/h on a course of 175 and ship D sailed at a speed of 18 km/h on a course of 85. (a) Sketch a diagram to show the relative positions of the ships and port O at 4 : 00 pm on the same day. (b) Find the whole circle bearing of ship D from ship C at that time, correct to the nearest degree. 8. car travels from town in the direction of S32 W towards town 45 km away. Several hours later, the car leaves and goes to town. The bearings of from and are S9 E and S58 E respectively. (a) How far should the car travel from town to reach town? (b) There is a town S which is due east of and due north of. (i) Find the distance between towns and S. (ii) Find the whole circle bearing of from S. 45 km (16 marks)
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