Answer:
AB=18km
Step-by-step explanation:
In any triangle in 2 dimensions our interior angles should equal to 180°.
We know 2 of the three interior angles, since we know it must sum up to 180° let's subtract these known interior angles to obtain:
180°-79°-68°=33°
Furthermore, since this triangle is not a right triangle we cannot use the Pythagorean equation. Therefore let's use the law of sines:
[tex]\frac{sin(A)}{a} =\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Where A is angle A=33°, B = 68°, C=79°, a = CB, b=AC, c=AB.
Since we want to find side AB and we know A, a, and C we only use 2 of those parts of the law of sines and so:
[tex]\frac{sin(33)}{10} =\frac{sin(79)}{AB}\\ \\AB*\frac{sin(33)}{10}=\frac{sin(79)}{AB}*AB\\\\AB*10*\frac{sin(33)}{10}=10*sin(79)\\\\AB*sin(33)=10*sin(79)\\\\\frac{AB*sin(33)}{sin(33)}=\frac{10*sin(79)}{sin(33)}\\ \\[/tex]
[tex]AB=\frac{10*sin(79)}{sin(33)} \\AB=18.02344\\AB=18km[/tex]
