   Chapter 5.5, Problem 6E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 5 to 22, find the missing lengths. Give your answers in both simplest radical form and as approximations correct two decimal places. Given: Right ∆ X Y Z with X Z ¯ ≅ Y Z ¯ and X Y = 10 Find: X Z and Y Z To determine

To find:

XZ and YZ for the right XYZ with XZ¯YZ¯ and XY=10.

Explanation

Approach:

For a right triangle for which the measure of the interior angles 45°, 45°, and 90°, if ‘a’ is the length of measure of one of the leg; opposite to the angle 45°, then the length of the other two sides is given by

Length of the other leg =a

Length of the hypotenuse =a2

In general

Length of the legs are equal.

Length of the hypotenuse =2× (Length of one of the legs)

Calculation:

Given,

The right XYZ with XZ¯YZ¯ and XY=10.

Since, two of the sides of the right triangle are congruent, the angles opposite to the sides must be equal and should be 45° each.

Thus, the XYZ become

Here, XY is the hypotenuse of the XYZ.

By the application of 45°-45°-90°

45°-45°-90° theorem.

In a right triangle whose angle measures 45°, 45°, and 90°, the legs are congruent and the hypotenuse has a length equal to the product of 2 and the length of either leg

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