Solution of Astronomical Problems, 



75 



(4) Given two angles and the included side. 



Ve may solve the polar triangle by (3), or else proceed 

 thus. Trace through F, coinciding with A, the arc ADB, and 

 that one of the lines ni which makes an angle wdth ADB 



equal to one of the given angles. Take PQ along ADB 

 equal to the given side. Turn the cloth in a counter-clockwise 

 direction till Q coincides with A, and trace through that one 

 o£ the lines m which makes an angle with ACB equal to the 

 other given angle. Measure the triangle PQR thus obtained 

 on the cloth. 



(5) Griven two sides and an angle not included. 



Trace throuoh P, coinciding- with A- the arc ADB, and 

 that one of the lines m which makes an angle with ADB equal 

 to the given angle. Take PQ along ADB equal to one of 

 the given sides. Turn the cloth till Q coincides with A^ and 

 find a point R (if any) in which that one of the lines I which 

 is at a distance from A equal to the other given side cuts the 

 line already on the cloth. Join QK and measure the 

 triangle PQR. 



The graphical solution shows at once when one solution, 

 two solutions, or no solutions are possible (in general, evi- 

 dently if QR lies between PQ and tt — PQ there is one 

 solution, otherwise two or no solutions). 



