In a right triangle, opposite=6 and hypotenuse=10. Find sin θ.
Answer: 3/5
Reasoning: sin θ=opposite/hypotenuse.
Reasoning: sin θ=opposite/hypotenuse.
Teacher Key · Unit 07 · Lesson 03
Law of Cosines
Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.
Khaemenes Academy · Teacher Key
Law of Cosines
Given a=7, A=35°, B=62°, find angle C.
Answer: 83°
Reasoning: Triangle angles sum to 180°.
Reasoning: Triangle angles sum to 180°.
Which law fits SAS data?
Answer: Law of Cosines
Reasoning: Two sides and included angle determine the opposite side.
Reasoning: Two sides and included angle determine the opposite side.
Find c when a=5, b=8, C=60°.
Answer: 7
Reasoning: c²=25+64−80(1/2)=49.
Reasoning: c²=25+64−80(1/2)=49.
Find the area with a=10, b=12, C=30°.
Answer: 30
Reasoning: K=½ab sin C.
Reasoning: K=½ab sin C.
A bearing of N35°E corresponds to what standard compass description?
Answer: 35° east of north
Reasoning: Read from north toward east.
Reasoning: Read from north toward east.