Question

A variables triangle
inscribed in a circle of radius R
if the rate of change
of a side is R times the rate of change of opposite angle then that angle is​

Answer 1

Answer:

hellow

Let ABC be a variable triangle inscribed in a circle of radius R.

Let the rate of change of a side is R times the rate of change of the opposite angle.

Let side

BC=a and

A be the opposite angle.

R=a2sinA

⇒a=2RsinA

Differentiate both sides with respect to

t, we get

dadt=2RcosAdAdt

⇒RdAdt=2RcosAdAdt

⇒cosA=12

⇒A=cos−1⁡(12)

⇒A=π3

Hence, the opposite angle is

π3.

I hope this helps you