For all $$\propto'_i{_s}, (i = 1, 2, 3, .....20)$$ lying between $$0^\circ  and  90^\circ$$, it is given that $$\sin \propto_1 + \sin  \propto_2 + \sin \propto_3 + .......+ \sin \propto_{20} = 20$$ What is the value (in degrees) of $$(\propto_1 + \propto_2 + \propto_3 + ......... + \propto_{20})$$ ?

$$\sin \propto_1 + \sin \propto_2 + \sin \propto_3 + .......+ \sin \propto_{20} = 20$$

As given that values will be between $$0^\circ$$  and $$90^\circ$$.

So $$sin 0^\circ = 0$$ and $$sin 90^\circ = 1$$

If each of the $$\propto$$ value is 90, then only the above given equation will be satisfied.

$$(\propto_1 + \propto_2 + \propto_3 + ......... + \propto_{20})$$

Here 90 will be 20 times. So 90$$\times\ $$20 = 1800