Question

• Provide full solutions, showing all of your steps. • Make sure that there is one step or idea per line. • Use one equal sign per line. • Make sure that equal signs line up vertically. • Don’t use self-developed short form notations. 1. Recall that "to solve a triangle" means to find values for all the angles and sides that weren't already given values. Using your knowledge of the sine and cosine laws, solve the following triangles. (5 marks each) a. Triangle ABC in which ?A = 65°, ?B = 35°, and AB = 7 units. b. Triangle XYZ in which x = 8.0 cm, y = 7.0 cm, and z = 5.5 cm. c. Triangle DEF in which ?D = 73°, d = 14 cm, and f = 10 cm. d. Triangle KMN in which k = 90 cm, n = 80 cm, and ?M = 50°. 2. The posts of a soccer (football) net are 7.50 m apart. A player is about to kick the ball to the net. If the ball is approximately 15 m from one post and 20 m from the other, within what angle does the player have to kick the ball for it to go into the net? (4 marks) 3. In a large harbour, the docks are labelled alphabetically and are built side by side in a straight line. Dock A and Dock K are located 2.3 km apart along this line. Dock L is on an island outside the harbour such that ?LAK is 45° and ?LKA is 64°. How far is the island dock away from each of the other two docks? (4 marks) 4. A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks) 5. It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)

• Provide full solutions, showing all of your steps.
• Make sure that there is one step or idea per line.
• Use one equal sign per line.
• Make sure that equal signs line up vertically.
• Don’t use self-developed short form notations.

1. Recall that "to solve a triangle" means to find values for all the angles and sides that weren't already given values. Using your knowledge of the sine and cosine laws, solve the following triangles. (5 marks each)
a. Triangle ABC in which ?A = 65°, ?B = 35°, and AB = 7 units.
b. Triangle XYZ in which x = 8.0 cm, y = 7.0 cm, and z = 5.5 cm.
c. Triangle DEF in which ?D = 73°, d = 14 cm, and f = 10 cm.
d. Triangle KMN in which k = 90 cm, n = 80 cm, and ?M = 50°.

2. The posts of a soccer (football) net are 7.50 m apart. A player is about to kick the ball to the net. If the ball is approximately 15 m from one post and 20 m from the other, within what angle does the player have to kick the ball for it to go into the net? (4 marks)

3. In a large harbour, the docks are labelled alphabetically and are built side by side in a straight line. Dock A and Dock K are located 2.3 km apart along this line. Dock L is on an island outside the harbour such that ?LAK is 45° and ?LKA is 64°. How far is the island dock away from each of the other two docks? (4 marks)

4. A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)

5. It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)

• Provide full solutions, showing all of your steps.
• Make sure that there is one step or idea per line.
• Use one equal sign per line.
• Make sure that equal signs line up vertically.
• Don’t use self-developed short form notations.

1. Recall that "to solve a triangle" means to find values for all the angles and sides that weren't already given values. Using your knowledge of the sine and cosine laws, solve the following triangles. (5 marks each)
a. Triangle ABC in which ?A = 65°, ?B = 35°, and AB = 7 units.
b. Triangle XYZ in which x = 8.0 cm, y = 7.0 cm, and z = 5.5 cm.
c. Triangle DEF in which ?D = 73°, d = 14 cm, and f = 10 cm.
d. Triangle KMN in which k = 90 cm, n = 80 cm, and ?M = 50°.

2. The posts of a soccer (football) net are 7.50 m apart. A player is about to kick the ball to the net. If the ball is approximately 15 m from one post and 20 m from the other, within what angle does the player have to kick the ball for it to go into the net? (4 marks)

3. In a large harbour, the docks are labelled alphabetically and are built side by side in a straight line. Dock A and Dock K are located 2.3 km apart along this line. Dock L is on an island outside the harbour such that ?LAK is 45° and ?LKA is 64°. How far is the island dock away from each of the other two docks? (4 marks)

4. A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)

5. It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)

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