A block of mass `M` si suspended by two strings angles `theta_(1)` and `theta_(2)` with the horizontal. Find the tensions in the strings.

Explanation

The block is in equilibrium, i.e. net force on it is zero.

By Lami's theorem
`(T_(1))/(sin(90+theta_(2)))=(T_(2))/(sin(90+theta_(1)))=(Mg)/(sin[180-(theta_(1)+theta_(2))])`
`(T_(1))/(costheta_(2))=(T_(2))/(costheta_(1))=(Mg)/(sin(theta_(1)+theta_(2)))`
OR
Resolving `T_(1)` and `T_(2)` in horizontal and vertical directions

`rarr:T_(1)costheta_(1)=T_(2)costheta_(2)` (i)
`uarr:T_(1)sintheta_(1)+T_(2)sintheta_(2)=Mg` (ii)
From (i) `T_(2)=(T_(1)costheta_(1))/(costheta_(2))` in (ii)
`T_(1)(sintheta_(1)costheta_(2)+costheta_(1)sintheta_(2))=Mgcostheta_(2)`
`T_(1)=(Mgcostheta_(2))/sin(theta_(1)+theta_(2))`
`T_(2)=(Mgcostheta_(1))/sin(theta_(1)+theta_(2))`