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

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 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 42E

To determine

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

Expert Solution & Answer

Answer to Problem 42E

The length of three sides of the right triangle are 3 , 13 and 2 .

Explanation of Solution

Given information:

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

Calculation:

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

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

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

The distance between the points (1,3,1) and (1,0,3) is,

Distance=(1−1)2+(0−3)2+(3−1)2=(0)2+(−3)2+(2)2=0+9+4=13

So, the length of the second side triangle is 13 .

The distance between the points (1,0,1) and (1,0,3) is,

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

So, the length of thethird side of triangle is 2 .

Therefore, the length of three sides of right triangle are 3 , 13 and 2 .

Let us check the Pythagorean Theorem.

P2+B2=H2

Take the left side of the equation.

P2+B2=(3)2+(2)2=9+4=13=(13)2

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

Chapter 10.1, Problem 41E

Chapter 10.1, Problem 43E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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