In this page rate of change question7 we are going to see solution of some practice question of the worksheet.

**Question 7:**

Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at the rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3.

**Solution:**

Let "b" and "h" be the base and height of the triangle ABC

Let θ radian be the angle between the sides AB and AC when b = 5 cm, c = 4 cm

dθ/dt = 0.06 radian/sec. Let "A" be the area of the triangle at time "t". From this we have to find the value of dA/dt when θ = π/3

Area of triangle ABC (A) = (1/2) b c sin θ

differentiating the whole equation with respect to "t"

dA/dt = (1/2) b c cos θ (dθ/dt)

at θ = π/3

= (1/2) (5) (4) (sin π/3) (0.06)

= (1/2) (20) (1/2) (0.06)

= (20/4) (0.06)

= 0.3 m²/sec

Therefore the area is increasing at the rate of 0.03 m²/sec

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- First Principles
- Implicit Function
- Parametric Function
- Substitution Method
- logarithmic function
- Product Rule
- Chain Rule
- Quotient Rule
- Rolle's theorem
- Lagrange's theorem
- Finding increasing or decreasing interval
- Increasing function
- Decreasing function
- Monotonic function
- Maximum and minimum
- Examples of maximum and minimum