Area and two angles

Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.

Correct result:

C =  119.5333 °
a =  20.8592
b =  55.309
c =  68.0557

Solution:

A=15+2860=2321515.4667 B=45 C=180AB=18015.466745=179315=119.5333=11932

Try calculation via our triangle calculator.

S=501.9 a=k u b=k v c=k w  w=1 u:w=sinA:sinC u=w sin(A)/sin(C)=1 sin(15.4667)/sin(119.5333)0.3065  v:w=sinB:sinC v=w sin(B)/sin(C)=1 sin(45)/sin(119.5333)0.8127  s=(u+v+w)/2=(0.3065+0.8127+1)/21.0596 T=s (su) (sv) (sw)=1.0596 (1.05960.3065) (1.05960.8127) (1.05961)0.1084 k=S/T=501.9/0.108468.0557 a=k u=68.0557 0.3065=20.8592
b=k v=68.0557 0.8127=55.309
c=k w=68.0557 1=68.0557



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