Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter - Section 11.4 - Applications with Acute Triangles - Exercises - Page 521: 43


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