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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Special Right Triangles

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Exercise 20 Page 645

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

x=15sqrt(3)/2, y=15/2

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.

15= 2 * y

.LHS /2.=.RHS /2.

15/2=y

Rearrange equation

y=15/2

We found that the measure of the shorter leg is 152. Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg. x=sqrt(3)* 15/2 ⇔ x=15sqrt(3)/2

Subchapter links

Exercises p.644-648