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1 Sine Law and Cosine Law Practice Questions Page 1 1. Mike needs to calculate the height of a tree that he will be removing from a construction site. The tree is leaning at an angle of 85 with the ground. Mike stands 30 meters from the base of the tree and calculates the angle of elevation to the top of the tree to be 32. What is the height of the tree? S"-')3 t hex_ St ;Litt 2-6 t 2to c_ c 0 14 * 2. --"A communications tower is stabilized with guy wires. One wire is 3.7 meters long. A second guy wire is attached to the pole 1.25 meters higher than the first wire, from the same anchor point on the ground. The angle made between the two wires is 10. What is the length of the second wire? c> i ka i t 2-s Lvt A- 3. ri9,14s' e 3 I (.,) sin (17/) 2,c 0 s'a

2 Sine Law and Cosine Law Practice Questions Page 2 3. Kat and Steve are hiking beside a creek. They are 20 meters apart when they spot a pika (small creature) on the opposite side of the creek. a) How far is Kat from the pika? tgo :1 sivhi _ b) How far is Steve from the pika? TO c) How wide is the creek? 500(R t4 tt d.) :3

3 Sine Law and Cosine Law Practice Questions Page 3 4. Alex is camping at a provincial park. He has taken a row boat out onto the lake. How far will he have to row if he travels from point A to point B, to point C, then back to point A? 906(3 6 o teali wee AA 3.(0 \. _ 4o of2

4 Sine Law and Cosine Law Practice Questions Page 4 5. Charlie is in a hot air balloon. His friends David and Eva are watching from the ground. David and Eva are standing 100 feet apart, and the angle between Charlie's line of sight to the two of them is 11. Eva is 505 feet from the balloon. What is the angle of elevation of David's line of sight to the balloon? t job

5 Sine Law and Cosine Law Practice Questions Page 5 6. A flag pole is stabilized using two guy wires. The wires are attached to the ground on opposite sides of the flag pole, 8 meters apart. The wire on the left is 4.7 meters long. The wire on the right is 6.0 meters long and is attached at an angle of elevation of 36. a) What is the angle of elevation of the wire on the left? 5 n 315 4,2 Vl IOLo b) How high up the flag pole are the wires attached? 3(0 ove

6 Sine Law and Cosine Law Practice Questions Page 6 7. The angle of elevation to the top of a tree from point B is 42. From point C, which is 70 meters closer to the tree, the angle of elevation to the top of the tree is 58. How tall is the tree? ID, b 0 OH II; Lb \d" S z\ r u c a 7f 4 4

7 Sine Law and Cosine Law Practice Questions Page 7 8. Alfred and Beverly are hiking when they notice people rock-climbing on a cliff nearby. They want to estimate the height of the cliff. Alfred estimates the angle of elevation to the top of the cliff from his location is about 45. Beverly is 15 meters closer to the cliff, and she estimates the angle of elevation to be 50. a) What is the distance from Alfred's location to the top of the cliff? 131. r-s b) What is the height of the cliff? 5u16 LIS c) How far from the base of the cliff is Alfred standing?

8 Sine Law and Cosine Law Practice Questions Page 8 9. The captain of a boat sees two points of land: point C is 1.8 kilometers east of the boat and point A is at a bearing of 12. If points A and C are 2.5 kilometers alcal -itiow far is the boat from point A? 5,A /F 50' ----r sica ya 00-/# -44lb 95(,2-7) Brent is a surveyor. He has been hired by city planners who are developing a park within the city. They want to build a bridge over a pond, so that a walking trail can be installed. Brent collects the following measurements. What is the length of the pond from A to B? Sy

9 Sine Law and Cosine Law Practice Questions Page Mary and Roxanne are going hiking through a park. They both leave from the same spot in the parking area. Mary follows one trail, walking 4.3 km/h in a direction 40 east of north. Roxanne follows a different trail, walking 4.8 km/h is a direction 52 east of south. How far apart are they after 2 hours? a Is- 12-t 12. A ship travels south from port for 2 hours at 35 km/h. It then changes course and travels 20 west of south for 3 hours at the same speed. How far is it from port after 5 hours? Port ita (ft 4, lb 2. si K R ca /OS Boat r v Ci 1.3 v 12 A \(-3Y.

10 Sine Law and Cosine Law Practice Questions Page Gary is a beach lifeguard. He must set up the buoys for a swimming competition. Swimmers will jump off the pier, swim around one buoy, change direction and swim around a second buoy, then head back to the pier. The first buoy is 300 meters from the pier, and the second is 200 meters from the pier. The angle between them is 60. How long is the swim route? yl 14. A lighthouse operator observes two ships at distances of 4.6 kilometers and 3.8 kilometers away. The angle between the lines of observation is 82. How far apart are the two ships?

11 Sine Law and Cosine Law Practice Questions Page A telephone pole is supported with guy wires. Two wires are attached at the same point on one side of the tower and fastened into the ground 4.6 meters apart. The first wire is 9.2 meters long and the second is 6.8 meters long. es '1.. i t-t q, GOC 501' 1D 4 a) At what angle of elevation is wire 1 installed? b) How high up the pole are the wires attached? c) How far from the base of the tower is wire 1 fastened to the ground?

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