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High School Math Calculus Precalculus with Limits: A Graphing Approach

Tofind: The lengths of the sides of right triangle. Prove that these lengths satisfy Pythagorean Theorem.

Tofind: The lengths of the sides of right triangle. 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 39E

To determine

Tofind:The lengths of the sides of right triangle. Prove that these lengths satisfy Pythagorean Theorem.

Expert Solution & Answer

Answer to Problem 39E

The length of three sides of right triangle are 25 , 29 and 3 .

Explanation of Solution

Given information:

The graph is shown below.

Precalculus with Limits: A Graphing Approach, Chapter 10.1, Problem 39E

Calculation:

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

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 (0,4,0) and (0,0,2) is,

Distance=(0−0)2+(0−4)2+(2−0)2=(0)2+(−4)2+(2)2=0+16+4=20=25

So, the length of perpendicular of triangle is 25 .

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

Distance=(−2−0)2+(5−0)2+(2−2)2=(−2)2+(5)2+(0)2=4+25+0=29

So, the length of hypotenuse of triangle is 29 .

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

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

So, the length of base of triangle is 3 .

Therefore, the length of three sides of right triangle are 25 , 29 and 3 .

Let us check the Pythagorean Theorem.

P2+B2=H2

Take the left side of the equation.

P2+B2=(25)2+(3)2=20+9=29=(29)2

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

Chapter 10.1, Problem 38E

Chapter 10.1, Problem 40E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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