   Chapter 11.2, Problem 30E

Chapter
Section
Textbook Problem

# Classifying a TriangleIn Exercises 29–32, find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. ( 4 , − 1 , − 1 ) , ( 2 , 0 , − 4 ) , ( 3 , 5 , − 1 )

To determine

To calculate: The lengths of the sides of the triangle with vertices (4,1,1),(2,0,4),(3,5,1) and determine the type of triangle.

Explanation

Given:

The vertices are (4,1,1),(2,0,4),(3,5,1)

Formula used:

The distance formula is D= (x2x1)2+(y2y1)2+(z2z1)2 .

Pythagoras formula, P2+B2=H2, where P is the perpendicular side, B is the base side and H is the hypotenuse.

Calculation:

Let points represented as A=(4,1,1),B=(2,0,4),C=(3,5,1)

Now

AB = (42)2 + (10)2 + (1(4))2=(2)2 + (1)2 + (3)2 =4+1+9 = 14

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