(1)
- Law of sines to solve for [tex]b[/tex]:
[tex]\dfrac{\sin72^\circ}{9.5}=\dfrac{\sin b^\circ}{7.1}\implies b\approx45.3[/tex]
- The sum of the measures of interior angles of any triangle is [tex]180^\circ[/tex]. Use this to solve for [tex]a[/tex]:
[tex]a+b+72=180\implies a\approx62.7[/tex]
- Law of cosines to solve for [tex]c[/tex]:
[tex]c^2=7.1^2+9.5^2-2\cdot7.1\cdot9.5\cos a\implies c\approx6.92[/tex]
(2)
- Sum of interior angles:
[tex]31+122+d=180\implies d=27[/tex]
- Law of sines to solve for [tex]e[/tex]:
[tex]\dfrac{\sin122^\circ}e=\dfrac{\sin31^\circ}{6.4}\implies e\approx10.54[/tex]
(3)
- Sum of interior angles:
[tex]75+37+f=180\implies f=68[/tex]
- Law of sines to solve for [tex]g[/tex] and [tex]h[/tex]:
[tex]\dfrac{\sin75^\circ}g=\dfrac{\sin f^\circ}{195}\implies g\approx203.15[/tex]
[tex]\dfrac{\sin37^\circ}h=\dfrac{\sin f^\circ}{195}\implies h\approx126.57[/tex]
Don't forget to provide units for the side lengths solved for above!
