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

2 Answers

4 votes

don't know it is complicated

User David Andrei Ned
by
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4 votes

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

User Thomas Bouldin
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