Page 149 - How To Solve Word Problems In Calculus

Solution

a

θ
b

Let θ represent the angle between the two sides. The area of
the triangle is

1
A(θ) = ab sin θ 0 ≤ θ ≤ π
2
1

Since a and b are constants, A (θ) = abcos θ. Setting the
2
derivative equal to 0 and solving, we obtain
1
0 = abcos θ
2
0 = cos θ

π
θ =
2

Since A(θ) is a continuous function and A(0) = A(π) = 0, the
π
absolute maximum area occurs when θ = (a right angle).
2

π π 1
Since sin = 1, A max = A = ab.
2 2 2
EXAMPLE 6
A man at point A on the shore of a circular lake of radius 1 mile
wants to reach point B on the shore diametrically opposite A.
If he can row a boat 3 mi/h and jog 6 mi/h, at what angle θ
with the diameter should he row in order to reach B in the
shortest possible time?

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