   Chapter 5.5, Problem 5E 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 m ∠ X = 45 ° and X Z = 8 Find Y Z and X Y To determine

To find:

YZ and XY for the right XYZ with mX=45° and XZ=8.

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 mX=45° and XZ=8.

The given triangle should be a 45°-45°-90° triangle since its is given that one of the acute angle mX of the right triangle is given as 45°

Thus,

mX=45°

Thus, the triangle become

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