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Worksheet 5.6

LAW OF COSINES and AREA OF A TRIANGLE

Use the Law of Cosines to solve the triangle. Round answers to two decimal places.

1. A = 135°, b = 4, c = 9 2. a = 11, b = 47, c = 52

3. To calculate the width of a pond (without getting wet) , a surveyor walks 250 meters from point A to point B,

then turns 75° and walks 220 meters to point C. Find the width of the pond.

4. In a softball game, a batter hits the ball to center field. The center fielder then throws the ball to third base.

The distance from the center fielder to home plate is 240 feet. The distance between the bases is 60 feet.

How far did the center fielder throw the ball? Note: The baseball “diamond” is a square.

5. Find the measure of the largest angle in a triangle with sides of 4, 5, and 6.

6. Find the area of triangle ABC if A = 47°, b = 32 ft, and c = 19 ft.

Find the area of the triangle with the given side lengths, if possible. If not possible, write “No triangle possible.”

7. a = 23, b = 19, c = 12 8. a = 13, b = 10, c = 2

9. A businessman wishes to buy a triangular lot in a busy downtown location. The lot frontages on the

three adjacent streets are 125, 280, and 315 ft. Find the area of the lot.

10. If a gallon of paint covers 400 square feet, how many gallons are needed to paint a triangular deck with

sides of 65 ft, 72 ft, and 88 ft?

11. Find the area of a regular nonagon (9 sides) inscribed in a circle of radius 10 inches.

12. A parallelogram has sides of 18 and 26 ft, and an angle of 39°.

a. Find the length of the shorter diagonal.

b. Find the area of the parallelogram.

13. Two trains leave a station on different tracks. The tracks make an angle of 125° with the station (C) as the vertex.

The first train (A) travels at an average speed of 100 km per hour, and the second train (B) travels at an average

speed of 65 kilometers per hour. How far apart are the trains after 2 hours?

14. A boat runs in a straight line for 3 km, then makes a 45° turn and goes for another 6 km.

How far is the boat from the starting point?

15. One diagonal of a parallelogram is 6 cm long, and the other is 13 cm long. They form an angle of 42° with

each other. how long are the sides of the parallelogram? Hint: The diagonals of a parallelogram bisect

each other.

16. You want to buy a triangular lot measuring 510 yards by 840 yards by 1120 yards. The price of the land is $2000

per acre. How much does the land cost? (1 acre = 4840 square yards.)

17. The distance from Chicago to St. Louis is 440 km, that from St. Louis to Atlanta 795 km, and that from Atlanta

to Chicago 950 km. What is the measure of the angle that has St. Louis as the vertex?

-----------------------

C

A

B

240 ft

2nd

CF

3rd

H

1st

60 ft

A

C

Station

B

45°

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