Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Additional and Advanced Exercises - Page 38: 9

Answer

See explanations.
1574527320

Work Step by Step

Step 1. Draw a vertical line from point $C$ and label the height as $h$, as shown in the figure. Step 2. We can find the height as $h=b\cdot sinA=a\cdot sinB$ Step 3. The area of the triangle can be written as $Area=\frac{1}{2}ch=\frac{1}{2}cb\cdot sinA=\frac{1}{2}ca\cdot sinB=$ Step 4. Repeat the above steps by drawing a vertical line from point $B$ to get $Area=\frac{1}{2}bh'=\frac{1}{2}bc\cdot sinA=\frac{1}{2}ba\cdot sinC$ Step 5. Thus we can obtain $Area=\frac{1}{2}ab\cdot sinC=\frac{1}{2}bc\cdot sinA=\frac{1}{2}ca\cdot sinB$
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