math problems need solution with explanations

Surv2002 – Environmental Surveying Assignment 1. – Out of 44. Worth 7% of your final mark. Show all your work. Neatness will be marked. (10%-4marks)

1. Solve the following Trigonometry equation. Your answers will be in letters. (10 marks) a. Solve for r, y, x, 𝜃 using equations. b. 𝑆𝑖𝑛 𝜃 =? c. cos𝜃 =? d. Tan 𝜃 =? e. Sec 𝜃 = ? f. Cot 𝜃 =? g. Csc 𝜃 = ? h. What quadrant is the resultant line P located in?

2. Let P = (1, −3) be a point on the terminal side of 𝜃 Find each of the six trigonometric functions of 𝜃. (10 marks) Solution: P = (1, −3) is a point on the terminal side of 𝜃.

a. 𝑆𝑖𝑛 𝜃 =? b. cos𝜃 =? c. Tan 𝜃 =? d. Sec 𝜃 = ? e. Cot 𝜃 =? f. Csc 𝜃 = ? g. r=? h. What similarities do you see with all your answers from a) to f)?

3. Solve for the following Triangle (10 marks)

a. 𝜃 , A= 𝜃, B, C, a, b, c b. 𝑆𝑖𝑛 𝜃 =? c. cos𝜃 =? d. Tan 𝜃 =? e. Sec 𝜃 = ? f. Cot 𝜃 =? g. Csc 𝜃 = ? h. What similarities do you see with all your answers from b) to g)?

4.

The irregular blue shape in the figure represents a lake. The distance across the lake, a, is unknown. To find this distance, a surveyor took the measurements shown in the figure. What is the distance across the lake? (4 marks)

437 m

Multiple Choice – (1 mark each)

Ch. 4 Laws of Sines and Cosines; Vectors

4.1 The Law of Sines

1 Use the Law of Sines to Solve Oblique Triangles

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the triangle. 1)

95° 3

50°

A) B = 35°, a = 4.01, c = 5.21 B) B = 35°, a = 5.21, c = 4.01 C) B = 40°, a = 4.01, c = 5.21 D) B = 30°, a = 5.21, c = 4.01

2)

10 25° 100°

A) C = 55°, a = 23.3, c = 19.38 B) C = 55°, a = 19.38, c = 23.3 C) C = 60°, a = 23.3, c = 19.38 D) C = 50°, a = 19.38, c = 23.3

Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 3) B = 49°

C = 115° b = 49

A) A = 16°, a = 17.9, c = 58.8 B) A = 14°, a = 58.8, c = 17.9 C) A = 16°, a = 19.9, c = 60.8 D) A = 14°, a = 60.8, c = 19.9

4) A = 21° B = 20° a = 13.8

A) C = 139°, b = 13.2, c = 25.3 B) C = 140°, b = 13.2, c = 25.3 C) C = 139°, b = 25.3, c = 13.2 D) C = 140°, b = 25.3, c = 13.2

5) A = 26°, B = 51°, c = 21 A) C = 103°, a = 9.4, b = 16.7 B) C = 103°, a = 16.7, b = 9.4 C) C = 103°, a = 46.7, b = 26.3 D) C = 97°, a = 9.3, b = 16.4

6) A = 11.2°, C = 131.6°, a = 83.2 A) B = 37.2°, b = 259, c = 320.3 B) B = 37.2°, b = 320.3, c = 259 C) B = 37.2°, b = 26.7, c = 21.7 D) B = 36.8°, b = 256.6, c = 320.3

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3) C = 110°, a = 2 yards, b = 9 yards A) 8 square yards B) 17 square yards C) 34 square yards D) 3 square yards

4) B = 10°, a = 4 feet, c = 7 feet A) 2 square feet B) 5 square feet C) 10 square feet D) 14 square feet

4 Solve Applied Problems Using the Law of Sines

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) A surveyor standing 70 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48°. How tall is the radio tower?

A) 21.06 meters B) 7.97 meters C) 7.56 meters D) 11.09 meters

2) Two tracking stations are on the equator 120 miles apart. A weather balloon is located on a bearing of N43°E from the western station and on a bearing of N19°W from the eastern station. How far is the balloon from the western station? Round to the nearest mile.

A) 129 miles B) 138 miles C) 99 miles D) 90 miles

3) To find the distance AB across a river, a distance BC of 1369 m is laid off on one side of the river. It is found that B = 106.2° and C = 17.1°. Find AB. Round to the nearest meter.

A) 482 meters B) 485 meters C) 403 meters D) 400 meters

4) A guy wire to a tower makes a 67° angle with level ground. At a point 36 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 39°. Find the length of the wire (to the nearest foot).

A) 48 feet B) 53 feet C) 96 feet D) 101 feet

5 Additional Concepts

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find a. If necessary, round your answer to the nearest hundredth.

1)

49°

39° 55

A) 18.73 B) 6.9 C) 6.66 D) 9.7

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3) C = 110°, a = 2 yards, b = 9 yards A) 8 square yards B) 17 square yards C) 34 square yards D) 3 square yards

4) B = 10°, a = 4 feet, c = 7 feet A) 2 square feet B) 5 square feet C) 10 square feet D) 14 square feet

4 Solve Applied Problems Using the Law of Sines

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) A surveyor standing 70 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48°. How tall is the radio tower?

A) 21.06 meters B) 7.97 meters C) 7.56 meters D) 11.09 meters

2) Two tracking stations are on the equator 120 miles apart. A weather balloon is located on a bearing of N43°E from the western station and on a bearing of N19°W from the eastern station. How far is the balloon from the western station? Round to the nearest mile.

A) 129 miles B) 138 miles C) 99 miles D) 90 miles

3) To find the distance AB across a river, a distance BC of 1369 m is laid off on one side of the river. It is found that B = 106.2° and C = 17.1°. Find AB. Round to the nearest meter.

A) 482 meters B) 485 meters C) 403 meters D) 400 meters

4) A guy wire to a tower makes a 67° angle with level ground. At a point 36 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 39°. Find the length of the wire (to the nearest foot).

A) 48 feet B) 53 feet C) 96 feet D) 101 feet

5 Additional Concepts

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find a. If necessary, round your answer to the nearest hundredth.

1)

49°

39° 55

A) 18.73 B) 6.9 C) 6.66 D) 9.7

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