Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter - Section 11.4 - Applications with Acute Triangles - Exercises - Page 529: 45

Answer

$A=\frac{1}{2} \times a \times b$ square inch.

Work Step by Step

By using the formula $A=\frac{1}{2} \times a \times b \times sin\gamma$ to calculate the area of the triangle, we can see that we have to maximize the $sin\gamma$. The maximum is 1 where $\gamma = 90^{\circ}$ So the maximum area of the triangle is $A=\frac{1}{2} \times a \times b \times 1$.
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