/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q .5. Why is the Law of Cosines a gene... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q .5. (page 811)

Why is the Law of Cosines a generalization of the Pythagorean theorem?

Short Answer

Expert verified

As the law of cosines isa2+b2=c2

Step by step solution

01

Step 1:Given information

the Law of Cosines

02

Step 2:Explaination

In a triangle with sides a,b and c , where胃 is the angle between the sides of length aand bthen

a2+b2-2abcos90掳=c2.

Usingcos90掳=0, the expressiona2+b2-2abcos90掳=c2reduces to

a2+b2-2ab(0)=c2

hence

a2+b2-2abcos90''=c2

a2+b2=c2

Which is Pythagoras theorem.

Hence, the law of cosines is the generalization of Pythagoras theorem.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

u脳wandw脳u

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649595165778" u=1,-2andv=-3,6

In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

u=2,0,-5,v=-3,7,-1

Why do we use the terminology "separable" to describe a differential equation that can be written in the form

If u, v and w are three vectors in 鈩�3, which of the following products make sense and which do not?

localid="1649346164463" (a)u路(v路w)(b)u路(v脳w)(c)u脳(v路w)(d)u脳(v脳w)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.