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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 71 Page 659

Notice that the given figure is a 45^(∘)-45^(∘)-90^(∘) triangle.

x=7sqrt(2), y=14

Practice makes perfect

Notice that the given right triangle has a marked angle measuring 45^(∘). Therefore, by the Triangle Angle Sum Theorem, the measure of the third angle must also be 45^(∘).

In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the value of each variable. x & =7sqrt(2) y & = sqrt(2) * 7sqrt(2) Finally, we can find the simplest expression for y.

y=sqrt(2) * 7sqrt(2)

CommutativePropMult

Commutative Property of Multiplication

y=7* sqrt(2) * sqrt(2)

sqrt(a)* sqrt(a)= a

y=7* 2

Multiply

y=14

Subchapter links

Exercises p.655-659