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?One side of a triangle is increasing at a rate of and a second side is decreasing at a
Chapter 12, Problem 47(choose chapter or problem)
One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is \(\pi / 6\) ?
Questions & Answers
QUESTION:
One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is \(\pi / 6\) ?
ANSWER:Step 1 of 2
The area is given by
x and y are the sides and the angle is and A is the area
Taking the derivative with respect to time, we have
Solving for , we get
So, substituting we have