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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 , 0 , 0 ) , ( 1 , 3 , − 2 ) and ( − 2 , − 1 , 4 ) , and check the triangle is a right triangle or an isosceles or neither.

Tofind: The lengths of the sides of triangle with vertices ( 5 , 0 , 0 ) , ( 1 , 3 , − 2 ) and ( − 2 , − 1 , 4 ) , 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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 10.1, Problem 45E

To determine

Tofind:The lengths of the sides of triangle with vertices (5,0,0) , (1,3,−2) and (−2,−1,4) , and check the triangle is a right triangle or an isosceles or neither.

Expert Solution & Answer

Answer to Problem 45E

The length of three sides of the triangle are 29 , 61 and 66 .The given triangle is neither an isosceles nor a right triangle.

Explanation of Solution

Given information:

The vertices of the triangle are (5,0,0) , (1,3,−2) and (−2,−1,4) .

Calculation:

The vertices of the right triangle are (5,0,0) , (1,3,−2) and (−2,−1,4) .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 (5,0,0) and (1,3,−2) is,

Distance=(1−5)2+(3−0)2+(−2−0)2=(−4)2+(3)2+(−2)2=16+9+4=29

So, the length of thefirst side of triangle is 29 .

The distance between the points (1,3,−2) and (−2,−1,4) is,

Distance=(−2−1)2+(−1−3)2+(4−(−2))2=(−3)2+(−4)2+(6)2=9+16+36=61

So, the length of the second side triangle is 61 .

The distance between the points (5,0,0) and (−2,−1,4) is,

Distance=(−2−5)2+(−1−0)2+(4−0)2=(−7)2+(−1)2+(4)2=49+1+16=66

So, the length of the third side of triangle is 66 .

Therefore, the length of three sides of triangle are 29 , 61 and 66 .

The lengths of all sides of triangle are different. Therefore, the given triangle is not an isosceles triangle.

Let us check the Pythagorean Theorem.

P2+B2=H2

No two combination of the lengths of sides of the triangle satisfy Pythagorean theorem.

Therefore, the triangle is neither an isosceles nor a right triangle.

Chapter 10.1, Problem 44E

Chapter 10.1, Problem 46E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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