10th Edition

ISBN: 9780134781945

Author: Demana

Publisher: PEARSON

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Equations and inequalities describe the relationship between two mathematical expressions.

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Textbook Question

Chapter 1.7, Problem 16E

In Exercises 15−20, write the specified quantity as a function of the specified variable. It will help in each case to draw a picture.

16. One leg of a right triangle is twice as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.

Expert Solution & Answer

Solution

Write the length of the hypotenuse as a function of the length of the shorter leg.

$H=5B2$

Given:

One leg of a right triangle is twice as long as the other.

Concept Used:

The Pythagoras theorem, also known as the Pythagorean Theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

Calculation:

Let the Hypotenuse, Base & Perpendicular is H, B & P respectively.

Pythagoras theorem-

$(hypotenuse) 2 = (base) 2 + (perpendicular) 2 (H) 2 = (B) 2 + (P) 2$

PRECALCULUS:GRAPHICAL,...-W/ACCESS, Chapter 1.7, Problem 16E

According to question −

Let length of shorter leg = P

And length of longer leg = B

One leg of a right triangle is twice as long as the other.

$B=2PP=B2$

$(H) 2 = (B) 2 + (P) 2 as P= B 2 (H) 2 = (B) 2 + ( B 2 ) 2 H2=B2+B42H2=4B2+B24H2=5B24H=5B24H=5B2$

So, the length of the hypotenuse as a function of the length of the shorter leg $H=5B2$

Chapter 1.7, Problem 15E

Chapter 1.7, Problem 17E

Chapter 1 Solutions

PRECALCULUS:GRAPHICAL,...-W/ACCESS

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Prob. 7QR Ch. 1.4 - Prob. 8QR Ch. 1.4 - Prob. 9QR Ch. 1.4 - Prob. 10QR Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.4 - Prob. 39E Ch. 1.4 - Prob. 40E Ch. 1.4 - Prob. 41E Ch. 1.4 - Prob. 42E Ch. 1.4 - Prob. 43E Ch. 1.4 - 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In Exercises 15−20, write the specified quantity as a function of the specified variable. It will help in each case to draw a picture. 16. One leg of a right triangle is twice as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg.

Solution Summary: The author explains the Pythagoras theorem, which states that the square of the hypotenuse is equal to the sum of squares of other two sides of a right-angled triangle.

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Chapter 1 Solutions