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In this video you will learn how to find the Rate of Change of an angle that is related to adjacent angles given the horizontal speed of the moving person and position of the person.

Two buildings, of height 20 feet and 40 feet, are 60 feet apart. Suppose that the intensity of light at a point between the buildings is proportional to the angle Ã˜ in the figure. If a person is moving from right to left at 4 feet per second, at what rate is this angle Ã˜ changing when the person is exactly halfway between the two buildings?

0:28 Expressing the given angle Ã˜ in terms of adjacent angles Ã˜1 and Ã˜2 - finding equation
2:10 Differentiating the equation implicitly
3:25 Working on each individual triangle - using given Info
4:54 Finding Trigonometric equations for each adjacent angle, Ã˜1 and Ã˜2, using each Triangle
5:26 Differentiating each Trigonometric equation implicitly
10:25 Filling in known quantities
12:20 Finding adjacent angles Ã˜1 and Ã˜2 using Trigonometry
16:00 Solving for Ã˜'(t) using known adjacent angles' primes Ã˜1'(t) and Ã˜2'(t)

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