Formative: Law of Sines and Cosines

Identify the Law of Sines

• $\sin^2x\ +\ \cos^2x\ =\ 1$

• $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

• $a^2=b^2+c^2-2bc\cos A$

• $SOH\ CAH\ TOA$

Find AC

• 12
• 10
• 23
• 14

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the measure of angle A?

• 50 degrees
• 60 degrees
• 78 degrees
• 74 degrees

Tags

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.D.11

solve the triangle:
A=65 C=65 a=12

• B=50, b=9.9, c=12
• B=50, b=10.1, c=12
• B=70, b=12.8, c=12
• B=40 b=11.2, c=12

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Solve each triangle. A=40, B=20, a=2

• C=120, b=1.06, c=2.69
• C=135, b= 1.56, c=2.50
• C= 120, b=2.68. c=3.26
• C=45, b=1.06, c=2

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many triangles can you make if A=53, b=6, and a=4?

• 0
• 1
• 2
• Infinitely many

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many triangles can you make if A=53, b=6, and a=5?

• 0
• 1
• 2
• Infinitely many

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How many triangles can you make if A=53, b=6, and a=7?

• 0
• 1
• 2
• Infinitely many

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle. Solve any resulting triangles.

a=4, b=5, A=60

• None

• One Triangle, B= 67, c=1.34, C=86

• Two Triangles, B₁=68 , B₂=72 , c₁= 4.35, c₂= 6.25 C₁= 80 C₂=39

• One Triangle, B= 12, c=3, C=45

Solve the Triangle(s): a = 14, b = 6, A = 27 deg.

• no triangle possible

• B = 14 deg, C = 21 deg, c = 8.7

• B = 52 deg, C = 102 deg, c = 11.2

• B = 52 deg, C = 102 deg, c = 11.2

  OR

  B = 128 deg, C = 26 deg, c = 5.0