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McGraw Hill Integrated II, 2012 View details

3. Special Right Triangles

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Exercise 3 Page 644

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

22

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 x. x = sqrt(2) * 11sqrt(2) Finally, we can find the simplest expression for x.

x=sqrt(2) * 11sqrt(2)

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Simplify right-hand side

CommutativePropMult

Commutative Property of Multiplication

x=11*sqrt(2)*sqrt(2)

MultSqrt

sqrt(a)* sqrt(a)= a

x=11* 2

Multiply

x=22