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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

6. Law of Cosines

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Exercise 10 Page 530

The Law of Cosines relates the cosine of each angle of a triangle to its side lengths.

88.5^(∘)

Practice makes perfect

For any △ ABC, the Law of Cosines relates the cosine of each angle to the side lengths of the triangle.

To find the missing side length, we will start by drawing a diagram to illustrate the situation.

We know that the lengths of DE, FD, and FE are 13, 27, and 24, respectively. With this information and using the Law of Cosines, we can write an equation to find ∠ E.

27^2= 24^2+ 13^2-2( 24)( 13)cos ∠ E

▼

Solve for cos ∠ E

Calculate power and product

729=576+169-624(cos ∠ E)

Add terms

729=745-624(cos ∠ E)

LHS-745=RHS-745

- 16=- 624(cos ∠ E)

.LHS /(- 624).=.RHS /(- 624).

- 16/-624=cos ∠ E

- a/- b=a/b

16/624=cos ∠ E

Calculate quotient

0.025641...=cos ∠ E

Rearrange equation

cos ∠ E=0.025641...

To find ∠ E, we will use the inverse operation of cos, which is cos ^(- 1). 0.02641=cos E ⇔ cos ^(- 1)0.02641=E Finally, we will use a calculator.

cos ^(- 1)0.025641=∠ E

Use a calculator

88.530717... ^(∘)=∠ E

Round to 1 decimal place(s)

88.5^(∘)≈ ∠ E

Rearrange equation

∠ E≈ 88.5^(∘)

Subchapter links

Lesson Check p.529

Practice and Problem-Solving Exercises p.530-532

Standardized Test Prep p.532

Mixed Review p.532