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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 11 Page 513

Use the formula for finding the area of a triangle using sine, 12ac sin B.

≈ 147.3 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=1/2ac sin B Since we are given that a= 20, c= 16, and m∠ B= 67^(∘), we can substitute these values into the formula to find the area. Let's do it!

Area=1/2ac sin B

SubstituteValues

Substitute values

Area=1/2( 20)( 16) sin 67^(∘)

▼

Simplify right-hand side

Multiply

Area=1/2(320) sin 67^(∘)

MoveRightFacToNumOne

1/b* a = a/b

Area=320/2 sin 67^(∘)

Calculate quotient

Area=160 sin 67^(∘)

Use a calculator

Area=160(0.920504... )

Multiply

Area=147.280776...

Round to 1 decimal place(s)

Area≈ 147.3

The area of △ ABC is about 147.3 square units.

Subchapter links

Communicate Your Answer p.507

Monitoring Progress p.508-512

Exercises p.513-516