PRECALCULUS HONORS TEST REVIEW
6.1 and 6.2
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both.
Round your answers to two decimal places.
1. B = 72 , C = 82 , b = 54
2. A = 95 , B = 45 , c = 104.8
3. B = 150 , a = 10, b = 3
4. A = 75 , a = 51.2, b = 33.7
Find the area of the triangle having the indicated angle and sides.
5. A = 27 , b = 5, c = 7
6. C = 123 , a = 16, b = 5
7. From a certain distance, the angle of elevation to the top of a building is 17º. At a
point 50 meters closer to the building, the angle of elevation is 31º. Approximate the
height of the building.
8. A tree stands on a hillside of slope 28º from the horizontal. From a point 75 feet down
the hill, the angle of elevation to the top of the tree is 45º. Find the height of the tree.
Use the Law of Cosines to solve the triangle. Round your answers to two decimal
places.
9. a = 5, b = 8, c = 10
10. a = 2.5, b = 5.0, c = 4.5
11. B = 110 , a = 4, c = 4
12. A = 62 , b = 11.34, c = 19.52
13. The lengths of the diagonals of a parallelogram are 10 feet and 16 feet. Find the
lengths of the sides of the parallelogram if the diagonals intersect at an angle of 28º.
14. To approximate the length of a marsh, a surveyor walks 425 meters from point A to
point B. Then the surveyor turns 65º and walks 300 meters to point C. Approximate
the length AC of the marsh.
15. Two planes leave Raleigh-Durham Airport at approximately the same time. One is
flying 425 miles per hour at a bearing of 355º, and the other is flying 530 miles per
hour at a bearing of 67º. Draw a figure that gives a visual representation of the
problem and determine the distance between the planes after they have flown for 2
hours.
16. Points A and B are on opposite sides of the Grand Canyon. Point C is 200 yards from
A. Angle B measures 87º37’ and angle C measures 67º12’. What is the distance
between A and B?
17. The lengths of two sides of a parallelogram are 24.6 inches and 38.2 inches. The
angle at one vertex has measure 108º42’. Find the lengths of the diagonals.
18. On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from
Orlando, and Denver is 235 mm from Niagara Falls. Find the bearing of Denver
from Orlando. Find the bearing of Denver from Niagara Falls.
Use Heron’s Area Formula to find the area of the triangle.
19. a = 4, b = 5, c = 7
20. a
12.3, b
15.8, c
3.7