Chapter 5.CT, Problem 9CT

### 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

# Given quadrilateral ABCD with diagonal A C - . If B C - ⊥ A B - and A C - ⊥ D C - , find DA if A B = 4 ,   B C = 3 ,   a n d   D C = 8 . Express the answer as a square root radical.

To determine

To find:

The value of DA.

Explanation

Â BCÂ¯âŠ¥ABÂ¯Â andÂ ACÂ¯âŠ¥DCÂ¯

AB=4,BC=3,andÂ DC=8

First, find the value of AC.

Consider the â–³ABC,

Here, AB=4,BC=3 are the legs

We have to find the hypotenuse AC.

By Pythagorean Theorem,

The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the length of the legs.

AC2=AB2+BC2

Substituting the values in the above equation,

AC2=42+32

A

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