Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 7, Problem 14CLR

To determine

To find: the length of the hypotenuse.

Expert Solution & Answer

Answer to Problem 14CLR

The length of the hypotenuse is 13cm .

Explanation of Solution

Given information:

One leg length of a right triangle is 8cm less than hypotenuse and other leg is 1cm less than the hypotenuse.

Calculation: to find the length of the hypotenuse,

Let x represents the length of the hypotenuse, so

One leg of right angle is x−8 cm and other leg is x−1 .

Now, use the Pythagoras theorem and simplify,

(x−8)2+(x−1)2=x2x2−16x+64+x2−2x+1=x2 [expand sqaure]2x2−18x+65=x2 [simplify]x2−18x+65=0 [subtract](x−13)(x−5)=0 [factorise]x≠5 [because the legs of the triangle can't be negative]x=13

Thus, The length of the hypotenuse is 13cm .

Chapter 7, Problem 13CLR

Chapter 7, Problem 15CLR

Chapter 7 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 7.1 - Prob. 1OE Ch. 7.1 - Prob. 2OE Ch. 7.1 - Prob. 3OE Ch. 7.1 - Prob. 4OE Ch. 7.1 - Prob. 5OE Ch. 7.1 - Prob. 6OE Ch. 7.1 - Prob. 7OE Ch. 7.1 - Prob. 8OE Ch. 7.1 - Prob. 9OE Ch. 7.1 - Prob. 10OE

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