Once you know the vertical reactions you can analise each of the pin joints in turn. For example at point C the vertical reaction is 18.75 but we know that the total reaction must be in the direction of C-D (otherwise the beam would rotate around its pin joints).
If we want the force to be directed down 4 units for every 5 horizontal force units then we need 5 units of force for every 4 units of horizontal force. That is 18.75 * 5 / 4 = 23.44.
A similar argument applies at B only here the ratio is 2.5/4.
The horizonta force at A can then be found by recognising that the sum of the horizontal forces must be zero (as the beam is not moving).
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Engineering Indeterminate Beam 
Linear Mode
