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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

7. Law of Sines and Law of Cosines

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Exercise 12 Page 513

Use the formula for finding the area of a triangle using sine, 12ab sin C.

≈ 52.2 square units

Practice makes perfect

We want to find the area of △ ABC.

To do so, we will use the formula for finding the area of a triangle using sine. Area=1/2ab sin C Since we are given that a= 7, b= 15, and m∠ C= 96^(∘), we can substitute these values into the formula to find the area. Let's do it!

Area=1/2ab sin C

SubstituteValues

Substitute values

Area=1/2( 7)( 15) sin 96^(∘)

▼

Simplify right-hand side

Multiply

Area=1/2(105) sin 96^(∘)

MoveRightFacToNumOne

1/b* a = a/b

Area=105/2 sin 96^(∘)

Calculate quotient

Area=52.5 sin 96^(∘)

Use a calculator

Area=52.5(0.994521... )

Multiply

Area=52.212352...

Round to 1 decimal place(s)

Area≈ 52.2

The area of △ ABC is about 52.2 square units.

Subchapter links

Communicate Your Answer p.507

Monitoring Progress p.508-512

Exercises p.513-516