Math1083Lab Worksheets 142 PDF

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Math 1083 Worksheet 14 Getting Ready for Solving Oblique Triangles – the Law of Cosines Objectives: 1. Solve trigonometric equations 2. Review the Pythagorean identities 3. Simplify expressions following PEMDAS 4. Identify SSA, AAS, SAS, SSS triangles #1 Find all solutions on the interval 0° ≤ ≤ 180° a) 2sin θ -1=0 Sin θ =0.5 Therefore, θ =300 and 1500 b) 2cos θ -√3=0 cos θ =√3/2 cos θ =1.7321 therefore, θ =300 c) -2sin θ +√3=0 sin θ =√3/2=0.8660 therefore, θ =600 d) 2cos θ +3=2 Cos θ =-0.5 Therefore, ⱺ=1200 #2. Simplify the expressions. a). 42+102-2(4) (10) (0.5) Cos600 16+100-80cos600 116-40 =76 b). 102=52+62-2(5)(6) cos θ

Do Not solve

100=25+36-60cosⱺ 39=-60cos θ cosⱺ=-60/39 cosⱺ=-0.65 #3. Solve the equation below for �. �2 = 72 + 82 − 2(7)(8) cos 45° a2=49+64-79.1959 a2=113-79.1959 a=√33.8142 a=5.81

Give all answer in degrees.

35 Six types of triangles based on given information

#4. Determine which type of triangle is given in each case. Draw a diagram to illustrate. Do NOT solve the triangles. a). a=4, b=5, c=8

SSS

a=4

b=5

c=8

b). a=23.1, b=20, A=340 SSA

a=23.1

340 b=20

A

c). a=6, c=8, B=400

SSA

B

a

400 6

C

8

c

A

d). B=350, C=550, a=12 AAS

A

350

550

B

a=12

e). A=750, b=8, C=200 ASA

A 750 b=8

200

C

f). b=12, c=16.5, A=650

SSA C

B

C

b

A

650

12

16.5

B

c

e) = 75°, = 8, � = 20°

f) = 12, = 16.5, � = 65°

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