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Barry you need a scientific calculator, one with buttons that has sin, cos, tan, on it. Sheeny has told you the correct thing. The sides and the angles opposite those sides are related by what is called the sine ratio which is abbreviated as sin.
The calculator has to be in degree mode. Generally displayed in the calculator window as either DEG or simply D.
In your image call the side opposite the side of 5m by the letter a.
Call the side opposite 71 degrees by the letter b and the side opposite 64 degrees by the letter c.
The angles in a triangle add to 180 degrees therefore the missing angle is the difference between 180 and the others added together (64+71) this gives 55 degrees.
To find side b write the ratio b/sin(71) = 5/sin(55)
Multiplying both sides of the equation by sin(71) will give you...
b=5 sin(71)/sin(55)
=5.7713252514678684467369091411063
to find c write the ratio c/sin(64) = 5/sin(55)
Muliplying both sides of the equation by sin(64) will give you...
c=5 sin(64)/sin(55)
=5.4861246612605534554725269426624
Hope that helps.
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