Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 324: 74


33 cans of paint are needed.

Work Step by Step

We can find the semi-perimeter $S$: $S = \frac{75+68+85}{2} = 114$ We can find the area: $A = \sqrt{S~(S-a)(S-b)(S-c)}$ $A = \sqrt{(114)~(114-75)(114-68)(114-85)}$ $A = \sqrt{(114)~(39)(46)(29)}$ $A = \sqrt{5,930,964}$ $A = 2435.36~m^2$ We can find the number of cans of paint which are required: $\frac{2435.36~m^2}{75~m^2} = 32.5~cans$ Therefore, 33 cans of paint are needed.
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