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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 19 Page 537

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

16.3 mm

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 length of the side TU. Consider the given triangle. Let the length of TU be v.

We know the length of two sides, 24 mm and 12mm, and that the measure of their included angle is 38^(∘). With this information we want to find the length of the third side v. We can use the Law of Cosines to write an equation in terms of v.

v^2= 24^2+ 12^2-2( 24)( 12)cos 38^(∘)

▼

Solve for v

Calculate power

v^2=576+144-2(24)(12)cos 38^(∘)

Use a calculator

v^2=576+144-2(24)(12)(0.78801...)

Multiply

v^2=576+144-453.89419...

Add and subtract terms

v^2=266.10580...

sqrt(LHS)=sqrt(RHS)

v=sqrt(266.10580...)

Calculate root

v=16.31274...

Round to 1 decimal place(s)

v≈ 16.3

Note that we only kept the principal root when solving the equation, because TU, or v, is the length of a side.