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High School Math Calculus PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Tofind: The lengths of the sides of triangle with vertices ( 5 , 3 , 4 ) , ( 7 , 1 , 3 ) and ( 3 , 5 , 3 ) , and check the triangle is a right triangle or an isosceles or neither.

Tofind: The lengths of the sides of triangle with vertices ( 5 , 3 , 4 ) , ( 7 , 1 , 3 ) and ( 3 , 5 , 3 ) , and check the triangle is a right triangle or an isosceles or neither.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 10.1, Problem 44E

To determine

Tofind:The lengths of the sides of triangle with vertices (5,3,4) , (7,1,3) and (3,5,3) , and check the triangle is a right triangle or an isosceles or neither.

Expert Solution & Answer

Answer to Problem 44E

The length of three sides of the triangle are 3 , 62 and 3 . The given triangle is an isosceles triangle.

Explanation of Solution

Given information:

The vertices of the triangle are (5,3,4) , (7,1,3) and (3,5,3) .

Calculation:

The vertices of the right triangle are (5,3,4) , (7,1,3) and (3,5,3) .The length of the sides of triangle is the distance between the vertices.

Use the distance formula for two points (x1,y1,z1) and (x2,y2,z2) .

Distance=(x2−x1)2+(y2−y1)2+(z2−z1)2

The distance between the points (5,3,4) and (7,1,3) is,

Distance=(7−5)2+(1−3)2+(3−4)2=(2)2+(−2)2+(−1)2=4+4+1=9=3

So, the length of the first side of triangle is 3 .

The distance between the points (7,1,3) and (3,5,3) is,

Distance=(3−7)2+(5−1)2+(3−3)2=(−4)2+(4)2+(0)2=36+36+0=72=62

So, the length of the second side triangle is 62 .

The distance between the points (5,3,4) and (3,5,3) is,

Distance=(3−5)2+(5−3)2+(3−4)2=(−2)2+(2)2+(−1)2=4+4+1=9=3

So, the length of the third side of triangle is 3 .

Therefore, the length of three sides of triangle are 3 , 62 and 3 .

The lengths of two sides of triangle are equal. Therefore, the given triangle is an isosceles triangle.

Chapter 10.1, Problem 43E

Chapter 10.1, Problem 45E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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