Exercise 23 Page 645

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

x=14sqrt(3)/3, y=28sqrt(3)/3

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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.

14=sqrt(3) * x

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Solve for x

DivEqn

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

14/sqrt(3)=x

ExpandFrac

a/b=a * sqrt(3)/b * sqrt(3)

14sqrt(3)/sqrt(3)* sqrt(3)=x

MultSqrt

sqrt(a)* sqrt(a)= a

14sqrt(3)/3=x

RearrangeEqn

Rearrange equation

x=14sqrt(3)/3

We found that the measure of the shorter leg is 14sqrt(3)3. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. y= 2 * 14sqrt(3)/3 ⇔ y=28sqrt(3)/3

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Exercises p.644-648

Exercise 23 Page 645

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