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A 13-foot ladder leaning against a building meets the side of the building exactly 12 feet above the ground. How far from the building is the base of the ladder rounded to the nearest hundredth foot?

User Sudheej
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1 Answer

4 votes

Answer:

At the moment in question, we have a 5-12-13 right triangle.

x^2 + y^2 = 13^2

2x dx/dt + 2y dy/dt = 0

2(5)(2/3) + 2(12) dy/dt = 0

dy/dt = -5/18 ft/s

the area is 1/2 xy, so

da/dt = 1/2 y dx/dt + 1/2 x dy/dt

= (1/2)((12)(2/3) + (5)(-5/18))

= 119/36

Explanation:

User Dsatish
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