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Solution
The correct answer was SSA and ASA. The sine law cannot always help you determine unknown angle measures or side lengths as in the SSS and SAS cases above. However there is another relationship we can use called the cosine law.
The Cosine Law:
The Cosine Law:
Proof of the Cosine Law
Proof of the Cosine Law
Print off the attached page and watch the video of the proof of the cosine law. Completed proof is also below.
Proof of the Cosine LawCompleted Cosine Law ProofActivity 4: "Where Do I Belong?"
Activity 4: "Where Do I Belong?"
This activity is designed to help you consolidate what you have learned. As you now have so many tools in your trigonometric toolbox, it can be overwhelming to figure which tool you should use. This hands-on activity should help with that! Cut out each of the cards attached. Each card will contain a triangle with information regarding the lengths of the sides and angles. Sort these cards on the template provided according to a specific strategy you would use to solve for the variable x.
“Why Do I Belong" Template“Why Do I Belong" CardsCheckpoint 2
Checkpoint 2
Way to go! You have almost finished the second of three sections for this unit. Complete the Checkpoint below before moving on to the final section.
To use the cosine law, what do you need to know about a triangle? There are two possible answers. Include both.
Either all three side length, or two side lengths and the angle enclosed between them.
Chloe is proving the cosine law. She begins by drawing an acute triangle as shown below. She knows she must come up with two equivalent expressions for h2. What are these two expressions? Hint: Do not use a primary trigonometric ratio.
h2=c2-x2 and h2=b2-y2
In triangle ABC, a=13.2 m, b = 9.6 m , c = 11.3 m. Find ∠C to the nearest hundredth.
∠C = 56.82°
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