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High School Math Calculus Precalculus with Limits: A Graphing Approach

Tofind: The lengths of the sides of right triangle and also prove that these lengths satisfy Pythagorean Theorem.

Tofind: The lengths of the sides of right triangle and also prove that these lengths satisfy Pythagorean Theorem.

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.1, Problem 40E

To determine

Tofind:The lengths of the sides of right triangle and also prove that these lengths satisfy Pythagorean Theorem.

Expert Solution & Answer

Answer to Problem 40E

The length of three sides of right triangle are 214 , 62 and 6 .

Explanation of Solution

Given information:

The graph is shown below.

Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 40E

Calculation:

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

Distance=(−2−2)2+(5−(−1))2+(0−2)2=(−4)2+(6)2+(−2)2=16+36+4=56=214

So, the length of perpendicular of triangle is 214 .

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

Distance=(−4−2)2+(4−(−1))2+(1−2)2=(−6)2+(5)2+(−1)2=36+25+1=62

So, the length of hypotenuse of triangle is 62 .

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

Distance=(−4−(−2))2+(4−5)2+(1−0)2=(−2)2+(−1)2+(1)2=4+1+1=6

So, the length of base of triangle is 6 .

Therefore, the length of three sides of right triangle are 214 , 62 and 6 .

Now let us check the Pythagorean Theorem.

P2+B2=H2

Take the left side of the equation.

P2+B2=(214)2+(6)2=56+6=62=(62)2

Hence, the lengths of the right triangle satisfy the Pythagorean Theorem.

Chapter 10.1, Problem 39E

Chapter 10.1, Problem 41E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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