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McGraw Hill Integrated II, 2012 View details

3. Special Right Triangles

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Exercise 18 Page 645

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

x=8, y=16

Practice makes perfect

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.

8sqrt(3)=sqrt(3) * x

DivEqn

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

8=x

RearrangeEqn

Rearrange equation

x=8

We found that the measure of the shorter leg is 8. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. y= 2 * 8 ⇔ y=16