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McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 70 Page 659

Notice that the given figure is a 30^(∘)-60^(∘)-90^(∘) triangle.

x=6, y=12

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Notice that the given right triangle has a marked angle measuring 60^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be 30^(∘).

In a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg.

6sqrt(3)=sqrt(3) * x

DivEqn

.LHS /sqrt(3).=.RHS /sqrt(3).

6=x

RearrangeEqn

Rearrange equation

x=6

We found that the measure of the shorter leg is 6. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. y= 2 * 6 ⇔ y=12

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Exercises p.655-659

Exercise 70 Page 659

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