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97. Geometry Consider a right triangle with a hypotenuse of 6 inches. 6 in. a. Show that the area of the right triangle is given by A(0) = 18 sin 0 cos 0. b. For what value of 0 is A(0) = 8 square inches. c. Without using a graphing utility, find the angle for which A(0) is maximized. If your calculator is in radian mode, convert your final answer to degrees.

97. Geometry Consider a right triangle with a hypotenuse of 6 inches. 6 in. a. Show that the area of the right triangle is given by A(0) = 18 sin 0 cos 0. b. For what value of 0 is A(0) = 8 square inches. c. Without using a graphing utility, find the angle for which A(0) is maximized. If your calculator is in radian mode, convert your final answer to degrees.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
**97. Geometry** Consider a right triangle with a hypotenuse of 6 inches. _Illustration_: The image shows a right triangle with: - Hypotenuse labeled as \( 6 \, \text{in.} \) - An angle labeled \( \theta \) **Tasks**: a. Show that the area of the right triangle is given by \( A(\theta) = 18 \sin \theta \cos \theta \). b. For what value of \( \theta \) is \( A(\theta) = 8 \) square inches. c. Without using a graphing utility, find the angle \( \theta \) for which \( A(\theta) \) is maximized. If your calculator is in radian mode, convert your final answer to degrees.
Transcribed Image Text:**97. Geometry** Consider a right triangle with a hypotenuse of 6 inches. _Illustration_: The image shows a right triangle with: - Hypotenuse labeled as \( 6 \, \text{in.} \) - An angle labeled \( \theta \) **Tasks**: a. Show that the area of the right triangle is given by \( A(\theta) = 18 \sin \theta \cos \theta \). b. For what value of \( \theta \) is \( A(\theta) = 8 \) square inches. c. Without using a graphing utility, find the angle \( \theta \) for which \( A(\theta) \) is maximized. If your calculator is in radian mode, convert your final answer to degrees.
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