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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 41E

To determine

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

Expert Solution & Answer

Answer to Problem 41E

The length of three sides of right triangle are 3 , 35 and 6 .

Explanation of Solution

Given information:

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

Calculation:

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

Distance=(2−0)2+(2−0)2+(1−0)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 (2,2,1) and (2,−4,4) is,

Distance=(2−2)2+(−4−2)2+(4−1)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 (0,0,0) and (2,−4,4) is,

Distance=(2−0)2+(−4−0)2+(4−0)2=(2)2+(−4)2+(4)2=4+16+16=6

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

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

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 right triangle satisfy the Pythagorean Theorem.

Chapter 10.1, Problem 40E

Chapter 10.1, Problem 42E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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