Answer:
third chord length is 27.8088 cm
Between III and I chord is [tex]27^\circ57'30''[/tex]
Between III and II chord is [tex]37^\circ36'30''[/tex]
Step-by-step explanation:
The calculation of measurements of the triangle is shown below:-
By Cosine rule
[tex]BC^2 = (14.32)^2 + (18.64)^2 - 2\times 14.32 \times 18.64 cos\114^\circ26'\\\\ BC^2 = 773.330156\\\\ BC = \sqrt{773.330156}[/tex]
BC = 27.8088 (it is the length of third chord)
By Sin rule
[tex]\frac{Sin A}{BC} = \frac{Sin B}{14.32} \\\\ \frac{Sin114^\circ26'}{27.8088} = \frac{Sin B}{14.32} \\\\ Sin B = \frac{14.32114^\circ26}{27.8088}[/tex]
After solving this we will get
Sin B = 0.468829
[tex]<B = Sin^{-1} 0.468829\\\\ <B = 27^\circ 57'30''[/tex]
Therefore
[tex]<A + <B + <C = 180^\circ[/tex]
[tex]<C = 180^\circ - 114^\circ26'-27^\circ57'30''\\\\ <C = 37^\circ36'30''[/tex]
Now,
third chord length is 27.8088 cm
Between III and I chord is [tex]27^\circ57'30''[/tex]
Between III and II chord is [tex]37^\circ36'30''[/tex]
The same is to be considered
