Question

Two sides of a triangle have lengths 4m and 5m. The measure of the angle between them is increasing at a rate of 0.05 rad/sec

Answer 1

your question is incomplete. A complete question is -----> Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at a rate of 0.05 rad/s. 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 :- from properties of triangle,
area of triangle , A = $\frac{1}{2}absin\theta$
here, a and b are side length of triangle and $\theta$ is angle between a and b.


here, a = 4, Ans b = 5 and $\frac{d\theta}{dt}=0.05rad/s$

now, A = 1/2 × 4 × 5 $sin\theta$

A = 10sin$\theta$

differentiate with respect to time,

dA/dt = 10cos$\theta$ × $\frac{d\theta}{dt}$

= 10 × cosπ/3 × 0.05

= 10 × 1/2 × 0.05 m²/s

= 0.25 m²/s