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McGraw Hill Integrated II, 2012 View details

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Exercise 37 Page 705

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

Practice makes perfect

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

Let's use this law to find the value of x. Consider the given triangle.

We know the three side lengths and want to find one of the interior angles of the triangle. We can use the Law of Cosines to write an equation in terms of x.

33.2^2= 53^2+ 21^2-2( 53)( 21)cos x^(∘)

▼

Solve for cos x^(∘)

CalcPow

Calculate power

1102.24=2809+441-2(53)(21)cos x^(∘)

AddTerms

Add terms

1102.24=3250-2(53)(21)cos x^(∘)

Multiply

1102.24=3250-2226cos x^(∘)

SubEqn

LHS-3250=RHS-3250

- 2147.76=- 2226cos x^(∘)

DivEqn

.LHS /(- 2226).=.RHS /(- 2226).

- 2147.76/- 2226=cos x^(∘)

DivNegNeg

- a/- b=a/b

2147.76/2226=cos x^(∘)

RearrangeEqn

Rearrange equation

cos x^(∘)=2147.76/2226

To find the value of x we will use the inverse operation of cos, which is cos ^(- 1). cos x^(∘)=2147.76/2226 ⇔ x=cos ^(- 1)(2147.76/2226) Finally, we will use a calculator.

x=cos ^(- 1)(2147.76/2226)

UseCalc

Use a calculator

x=15.23595...

RoundInt

Round to nearest integer

x≈ 15

Subchapter links

1 Geometric Mean p.703

2 The Pythagorean Theorem and Its Converse p.703

3 Special Right Triangles p.704

4 Trigonometry p.704

5 Angles of Elevation and Depression p.705

6 The Law of Sines and Law of Cosines p.705

7 Vectors p.706

8 Dilations p.706

Exercise 37 Page 705

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