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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 4 Page 537

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

x=4sqrt(3), y=8sqrt(3)

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 longer leg is sqrt(3) times the length of the shorter leg.

12=sqrt(3) * x

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Solve for x

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

12/sqrt(3)=x

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

12sqrt(3)/sqrt(3)* sqrt(3)=x

sqrt(a)* sqrt(a)= a

12sqrt(3)/3=x

a/b=.a /3./.b /3.

4sqrt(3)=x

Rearrange equation

x=4sqrt(3)

We found that the measure of the shorter leg is 4sqrt(3). Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. y= 2 * 4sqrt(3) ⇔ y=8sqrt(3)