   Chapter 5.5, Problem 2E 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

For the 45 ° - 45 ° - 90 ° triangle shown, suppose that A B = a 2 . Find: a) A C b) B C To determine

a) To find:

AC, for the 45°-45°-90° triangle shown, suppose that AB=a2.

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,

A 45°-45°-90° triangle ABC with AB=a2.

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

To determine

b) To find:

BC, for the 45°-45°-90° triangle shown, suppose that AB=a2.

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