Review of Law of Sines with Area of a Triangle

Review of Law of Sines with Area of a Triangle

GOAL: To solidify our understanding of Law of Sines and find the area of a triangle using the sine function.​

Multiple Choice

Use the LAW OF SINES to to find the length of "a."

• a = 33

• a = 24

• a = 12

• a = 29

Multiple Choice

Use the LAW OF SINES to find the length of "c."

• c = 10.08

• c = 8.05

• c = 6.09

• c = 4.9

Multiple Choice

Use the LAW OF SINES to find the measure of A.

• 28.34^o

• 40^o

• 77.8^o

• 36.9^o

Multiple Choice

Which of the following is NOT TRUE about the parts to the triangle?

• C = 69^o

• b = 26.95 units

• a = 26.00 units

• b = 31.10 units

Multiple Choice

Ignoring the find $$m\angle A$$  , which of the following is NOT TRUE about the parts to the triangle?

• c = 38.5 units

• B = 28.0^o

• c = 18.0 units

• A = 25.0^o

Finding the area WITHOUT knowing the height!!

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Since we know something about angle B (for the whole triangle) and c (for the whole triangle) we can find the height!​

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BUT WAIT! What if...

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We know something about angle C (for the whole triangle) and b (for the whole triangle) we can find the height!​

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SAME TRIANGLE, slightly different equation!​

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SO...​

​In general...if we know the lengths of two sides of a triangle AND the measure of the included angle, we can find the area!​

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​Area = (product of the two sides)(sin(included angle)) all divided by 2!

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Multiple Choice

Do we know the length of two sides and the included angle???

• YES;

  $$Area=\frac{11\cdot14\cdot\sin54}{2}$$  

• NO; we need more information

Multiple Choice

Find the area of ABC to the nearest tenth.

• 62.3 units²

• 124.6 units²

• 77.0 units²

• 100 units²

Multiple Choice

What is the area of this triangle?

• 14.494 meters squared
• 108.184 meters squared
• 54.092 meters squared
• 54.35 meters squared