Question

How do you solve the triangle given `A=55^circ, B=42^circ, c=3/4`?

Answer 1

`BC=0.619,AC=0.506`

Explanation:

Let the top angle be`color(white)(aaaaaaaa)` `55°=angle A`
Let the bottom left angle be`color(white)(aa)` `42°=angleB`
Let the bottom Right angle be`color(white)(a)` `83°=angleC`
Let the left side `color(white)(aaaaaaaaaa)` `=AB(c)`
Let the bottom side`color(white)(aaaaaaaa)` `=BC(a)`
Let the Right side`color(white)(aaaaaaaaaa)` `=AC(b)`

`:.180°-(55°+42°)=83°angleC`

`:.(AC)/SinB=(AB)/SinC`

`:.(AC)/Sin42°=(AB)/Sin83°`

multiply L.H.S. and R.H.S. by`color(blue)(color(white)(a)` `color(blue)(sin42°`

`:.color(blue)cancelsin(42°)^1/1 xx (AC)/cancel(sin42°)=(0.75)/Sin83° xx color(blue)(Sin42°)/1`

`:.AC=(0.75 xx 0.669130606)/(0.992546151)`

`:.AC=0.501847954/0.992546151`

`:.AC=0.505616745`

to the nearest 3 decimal places

`:.color(blue)(AC=0.506`

`:.(BC)/SinA=(AB)/SinC`

`:.(BC)/Sin42°=(AB)/Sin83°`

multiply L.H.S. and R.H.S. by`color(blue)(color(white)(a)` `color(blue)(sin55°`

`:.color(blue)cancelsin(55°)^1/1 xx (BC)/cancel(sin55°)=(0.75)/Sin83° xx color(blue)(Sin55°)/1`

`:.BC=(0.75 xx 0.8191522044)/(0.992546151)`

`:.BC=0.614364033/0.992546151`

`:.BC=0.6189778`

to the nearest 3 decimal places

`:.color(blue)(BC=0.619`