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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 72 Page 659

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

x=7sqrt(3), y=7

Practice makes perfect

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

In a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg.

14= 2 * y

.LHS /2.=.RHS /2.

7=y

Rearrange equation

y=7

We found that the measure of the shorter leg is 7. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg. x=sqrt(3) * 7 ⇔ x=7sqrt(3)

Subchapter links

Exercises p.655-659