Chapter 5.5, Problem 2E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 45Â°, 45Â°, and 90Â°, if â€˜aâ€™ is the length of measure of one of the leg; opposite to the angle 45Â°, 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 =2Ã— (Length of one of the legs)

Calculation:

Given,

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

45Â°-45Â°-90Â° theorem.

In a right triangle whose angle measures 45Â°, 45Â°, and 90Â°, 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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