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

Tofind: The lengths of the sides of triangle with vertices ( 1 , − 2 , − 1 ) , ( 3 , 0 , 0 ) and ( 3 , − 6 , 3 ) , and check the triangle is a right triangle or an isosceles or neither.

Tofind: The lengths of the sides of triangle with vertices ( 1 , − 2 , − 1 ) , ( 3 , 0 , 0 ) and ( 3 , − 6 , 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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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 46E

To determine

Tofind:The lengths of the sides of triangle with vertices (1,−2,−1) , (3,0,0) and (3,−6,3) , and check the triangle is a right triangle or an isosceles or neither.

Expert Solution & Answer

Answer to Problem 46E

The length of three sides of the triangle are 3 , 35 and 6 .The given triangle is a right triangle.

Explanation of Solution

Given information:

The vertices of the triangle are (1,−2,−1) , (3,0,0) and (3,−6,3) .

Calculation:

The vertices of the right triangle are (1,−2,−1) , (3,0,0) and (3,−6,3) .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 (1,−2,−1) and (3,0,0) is,

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

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

The distance between the points (3,0,0) and (3,−6,3) is,

Distance=(3−3)2+(−6−0)2+(3−0)2=(0)2+(−6)2+(3)2=0+36+9=45=35

So, the length of the second side triangle is 35 .

The distance between the points (1,−2,−1) and (3,−6,3) is,

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

So, the length of the third side of triangle is 6 .

Therefore, the length of three sides of the triangle are 3 , 35 and 6 .

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

Take the left side of the equation.

P2+B2=(3)2+(6)2=9+36=45=(35)2

Hence the lengths of the triangle satisfy the Pythagorean Theorem.

Therefore, the triangle is a right triangle.

Chapter 10.1, Problem 45E

Chapter 10.1, Problem 47E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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