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Math 1113 Quiz 4 Practice Summer 2008
Name: Last ____________________. First ____________________
You must show your work and/or provide explanations for your answers for all questions.
Otherwise, no credit will be given.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value of the indicated trigonometric function of the angle θ in the figure. Give an exact answer with a rational denominator.
Find sin θ.
A) sin θ = 58 7
B) sin θ = 58 3
C) sin θ = 7 58 58
D) sin θ = 3 58 58
Find tan θ.
A) 109 B) 9 1919 C) 1019 19 D) 1019
Solve the right triangle using the information given. Round answers to two decimal places, if necessary.
- b = 5 , B = 25 °; Find a, c, and A. A) a = 10. c = 11. A = 65°
B) a = 10. c = 12. A = 75°
C) a = 10. c = 11. A = 75°
D) a = 10. c = 12. A = 65°
- b = 8 , A = 25 °; Find a, c, and B. A) a = 3. c = 9. B (^) =65°
B) a = 4. c = 9. B (^) = 65°
C) a = 4. c = 8. B (^) = 65°
D) a = 3. c = 8. B (^) = 65°
Solve the problem.
- A building 150 feet tall casts a 30 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) A) 12 ° B) 11 ° C) 78 ° D) 79 °
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
- In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at 0.314 arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 150,000,000 km and
θ = 0.314 seconds = 0. 60
minutes = 0. 60 · 60
degrees
determine the distance d from Earth to 61 Cygni using Bessel's figures.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
- A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from port? Round your answer to the nearest 0.1°. A) S23.6°W B) N23.6°E C) S24.6°W D) N24.6°E
Solve the problem.
- A rocket tracking station has two telescopes A and B placed 1.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of 26° and telescope B reports an angle of elevation of 48°? A) 2.18 mi B) 1.86 mi C) 0.65 mi D) 1.29 mi
- To find the distance AB across a river, a distance BC of 1353 m is laid off on one side of the river. It is found that B = 112.9° and C = 13.2°. Find AB. Round to the nearest meter. A) 313 m B) 310 m C) 382 m D) 385 m
Solve the triangle.
A) b = 7.44, A = 137.2°, C = 7.8° B) b = 9.44, A = 7.8°, C = 137.2° C) b = 8.44, A = 7.8°, C = 137.2° D) b = 8.44, A = 137.2°, C = 7.8°
- a = 70 , b = 12 , C = 105 ° A) c = 74.02, A = 66 °, B = 9 ° B) c = 79.82, A = 64 °, B = 11 ° C) c = 76.92, A = 68 °, B = 7 ° D) no triangle
A) A = 125.1°, B = 24.1°, C = 30.8° B) A = 30.8°, B = 125.1°, C = 24.1°
C) A = 125.1°, B = 30.8°, C = 24.1° D) A = 30.8°, B = 24.1°, C = 125.1°
- a (^) = 9 , b (^) = 13 , c (^) = 16 A) A (^) = 34.2°, B (^) = 54.3°, C (^) = 91.5° B) A (^) = 32.2°, B (^) = 54.3°, C (^) = 93.5° C) A (^) = 36.2°, B (^) = 52.3°, C (^) = 91.5° D) no triangle
Solve the problem.
- In flying the 75 miles from Champaign to Peoria, a student pilot sets a heading that is 11 ° off course and maintains an average speed of 100 miles per hour. After 15 minutes, the instructor notices the course error and tells the student to correct his heading. Through what angle will the plane move to correct the heading and how many miles away is Peoria when the plane turns? A) 16.4°; 66.4 mi B) 16.4°; 50.68 mi C) 163.6°; 66.4 mi D) 163.6°; 50.68 mi
- Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 23 mph in a direction 330°. The second sails at 34 mph in a direction 190°. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats? A) 80.5 mi B) 84.2 mi C) 90.3 mi D) 107.4 mi
Find the area of the triangle. If necessary, round the answer to two decimal places.
95° 1 7
A) 3.49 B) 4.29 C) 0.31 D) 13.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
- Find the area of the shaded portion ( see illustration) of a circle of radius 25 cm, formed by a central angle of 115°. Round your answer to the nearest square cm.
[Hint: Subtract the area of the triangle from the area of the sector of the circle to obtain the area of the shaded portion.]
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
- A painter needs to cover a triangular region 63 meters by 68 meters by 71 meters. A can of paint covers 70 square meters. How many cans will be needed? A) 318 cans B) 3 cans C) 28 cans D) 14 cans
Answer Key
Testname: MATH1113-Q4-PRACTICE-SUMMER 2008
1) C
2) B
3) A
4) D
5) B
- 9.85 × 1013 km (More recent observations have refined this value to about 1.08 × 1014 km.)
- A
- D
- C
- B
- D
- C
- D
- C
- C
- A
- C
- A
- B
- D
- A
- 344 sq. cm
- C
- A
