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: 305 ft

Step-by-step explanation:

Given

[tex]\angle A=30^{\circ}[/tex]

[tex]\angle B=50^{\circ}[/tex]

[tex]c=600\ ft[/tex]

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

[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}\\\Rightarrow \angle C=180^{\circ}-30^{\circ}-50^{\circ}\\\Rightarrow \angle C=100^{\circ}[/tex]

Now using Sine law i.e.

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\Rightarrow \dfrac{a}{\sin 30^{\circ}}=\dfrac{600}{\sin 100^{\circ}}\\\\\Rightarrow a=600\times \dfrac{\sin 30^{\circ}}{\sin 100^{\circ}}=600\times 0.5077\\\\\Rightarrow a=304.62\ ft\approx 305\ ft[/tex]

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