Question

Use the law of sines to find m

Answer 1

Answer: 5.22

Explanation:

Given

`\angle A=103^(\circ)`

Sine law is
`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)\\`

Here, a=8, c=5

Putting values

`\Rightarrow (8)/(\sin 103)=(5)/(\sin C)\\\\\Rightarrow \sin C=(5)/(8)\sin 103^(\circ)=0.6089\\\Rightarrow C=37.51^(\circ)`

`\Rightarrow \angle B=180^(\circ) -103^(\circ)-37.51^(\circ)\\\Rightarrow \angle B=39.49^(\circ)`

If b=m, then

`\Rightarrow (8)/(\sin 103^(\circ))=(m)/(\sin 39.49^(\circ))\\\\\Rightarrow m=(\sin 39.49^(\circ))/(\sin 103^(\circ))* 8=5.22`