Question

Calculate the letters

Answer 1

(1)
- Law of sines to solve for
`b`:


`(\sin72^\circ)/(9.5)=(\sin b^\circ)/(7.1)\implies b\approx45.3`

- The sum of the measures of interior angles of any triangle is
`180^\circ`. Use this to solve for
`a`:


`a+b+72=180\implies a\approx62.7`

- Law of cosines to solve for
`c`:


`c^2=7.1^2+9.5^2-2\cdot7.1\cdot9.5\cos a\implies c\approx6.92`

(2)
- Sum of interior angles:


`31+122+d=180\implies d=27`

- Law of sines to solve for
`e`:


`\frac{\sin122^\circ}e=(\sin31^\circ)/(6.4)\implies e\approx10.54`

(3)
- Sum of interior angles:


`75+37+f=180\implies f=68`

- Law of sines to solve for
`g` and
`h`:


`\frac{\sin75^\circ}g=(\sin f^\circ)/(195)\implies g\approx203.15`

`\frac{\sin37^\circ}h=(\sin f^\circ)/(195)\implies h\approx126.57`

Don't forget to provide units for the side lengths solved for above!