Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 5 Page 514

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

x=4sqrt(3), y=6

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.
y=sqrt(3) * 2sqrt(3)
Solve for y
y=2* sqrt(3)* sqrt(3)
y=2* 3
y=6
We found that the measure of the longer leg is 6. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. x= 2 * 2sqrt(3) ⇔ x=4sqrt(3)