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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 27 Page 656

Draw and label the side lengths of a 30^(∘)-60^(∘)-90^(∘) triangle.

1/2 or 0.5

Practice makes perfect

Let's begin with drawing a 30^(∘)-60^(∘)-90^(∘) triangle. If we call the shorter leg of this right triangle x, then the longer leg is xsqrt(3) and the hypotenuse is 2x.

In our exercise we are asked to evaluate the cosine of 60^(∘). Recall that the cosine of ∠ A is the ratio of the length of the leg adjacent ∠ A to the length of the hypotenuse. Using this definition, we can write the appropriate ratio for 60^(∘).

cos 60^(∘)=x/2x

a/b=.a /x./.b /x.

cos 60^(∘)=1/2

Write as a decimal

cos 60^(∘)=0.5

The cosine of 60^(∘) is 12 or 0.5.

Subchapter links

Exercises p.655-659