In the triangle shown above if increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per min when x = 3 units?

Solution:

The right angled triangle representing the problem statement is given below.

dθ/dt = 3 radians/minute (Increase at a constant rate) --- (1)

From the diagram above

sinθ = x/5

x = 5 sinθ

dx/dt = 5cosθ dθ/dt

From (1) dθ/dt = 3 radians/minute

dx/dt = 5cosθ(3) = 15cosθ --- (2)

Since it is a right angled triangle above

5² = x² + Base²

x = 3 units

Base² = 5² - 3²

Base² = 25 - 9 =16

Base = 4 units

cosθ = Base/hypotenuse = 4/5

Substitute the above value in equation (2)

dx/dt = 15(4/5)

= 12 units/minute

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In the triangle shown above if increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per min when x = 3 units?

Summary:

In the triangle shown above when increases at a constant rate of 3 radians per minute, the rate at which x increases in units per min when x = 3 units is dx/dt = 12 units/minute.