Chapter 5.5, Problem 15E

### 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

# In Exercises 15 to 19, create drawings as needed. Given: ∆ A B C with m ∠ A = m ∠ B = 45 ° and B C = 6 Find: A C and A B

To determine

To find:

AC and AB, for the ABC with mA=mB=45° and BC=6.

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,

âˆ†ABC with mâˆ A=mâˆ B=45Â° and BC=6.

Since, two of the angles mâˆ A and mâˆ B are 45Â°, the triangle is a right triangle of 45Â°-45Â°-90Â° type with BC=6.

45Â°-45Â°-90Â° theorem

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