This document is a comprehensive worksheet focused on the Law of Cosines, designed for students studying trigonometry. It includes various problems that require solving for unknown sides and angles in triangles, as well as real-world applications such as navigation scenarios. The worksheet is structured into sections, with problems labeled A through F, and provides a corresponding answer key for self-assessment. Key topics covered include the use of the Law of Cosines, triangle properties, and area calculations. The document is suitable for educational purposes, particularly for homework assignments or exam preparation. It serves as a valuable resource for both students and educators in mathematics. No specific author or publisher is mentioned in the provided content.
LAW OF COSINES WORKSHEET
1. Solve for the unknown in each triangle. Round to the nearest hundredth.
A. B. C.
D. E. F.
2. Solve for all missing sides and angles in each triangle. Round to the nearest
hundredth. ** USE PROPER VARIABLES
A.
122,15,29: ZmymxXYZ
B.
cmicmhcmgGHI 15,8,13:
C.
62,28,31: MmomnMNO
3. A triangle has sides equal to 4 m, 11 m and 8 m. Find its angles (round answers to
nearest tenth)
4. A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the
ship adjusts its course on a bearing of N 20º E. How far is the ship from the port at
4pm? (round to the nearest unit).
5. Find the area of the triangle whose sides are 12cm., 5cm. and 13cm.
θ
x
9.4cm
θ
47mm
42°
22m
17m
7cm
x
20m
47°
23m
8.3m
x
55cm
61°
35mm
39mm
13cm
50cm
θ
9.1m
4.9m
LAW OF COSINES WORKSHEET ANSWER KEY
1. Solve for the unknown in each triangle. Round to the nearest hundredth.
A. B. C.
D. E. F.
2. Solve for all missing sides and angles in each triangle. Round to the nearest
hundredth. ** USE PROPER VARIABLES
A.
122,15,29: ZmymxXYZ
z=39.08m <X= 38.99
o
<Y =19.01
o
B.
cmicmhcmgGHI 15,8,13:
<G=60
o
<H=32.20
o
<I=87.80
o
C.
62,28,31: MmomnMNO
m=30.50 <N=63.83
o
<O=54.16
o
3. A triangle has sides equal to 4 m, 11 m and 8 m. Find its angles (round answers to
nearest tenth) 16.21
o
, 129.84
o
, 33.95
o
4. A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the
ship adjusts its course on a bearing of N 20º E. How far is the ship from the port at
4pm? (round to the nearest unit). 88.79 miles
5. Find the area of the triangle whose sides are 12cm., 5cm. and 13cm. 30.00 cm
2
θ=103.91
x=14.7
9.4cm
θ= 46.90
o
47mm
42°
22m
17m
7cm
x=17.37
o
20m
47°
23m
8.3m
x=53.47
o
55cm
61°
35mm
39mm
13cm
50cm
θ=32.30
o
9.1m
4.9m
End of Document
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