Question

For ABC, let c = 600 ft, m angle B = 50° and then m angle A =30° Then a= ft. Round to nearest whole number.

Answer 1

don't know it is complicated

Answer 2

Answer: 305 ft

Explanation:

Given

`\angle A=30^(\circ)`

`\angle B=50^(\circ)`

`c=600\ ft`

From the angle sum property of the triangle, we can write

`\Rightarrow \angle A+\angle B+\angle C=180^(\circ)\\\Rightarrow \angle C=180^(\circ)-30^(\circ)-50^(\circ)\\\Rightarrow \angle C=100^(\circ)`

Now using Sine law i.e.

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

`\Rightarrow (a)/(\sin 30^(\circ))=(600)/(\sin 100^(\circ))\\\\\Rightarrow a=600* (\sin 30^(\circ))/(\sin 100^(\circ))=600* 0.5077\\\\\Rightarrow a=304.62\ ft\approx 305\ ft`