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

Answer: 305 ft

Step-by-step 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.

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

$\Rightarrow \dfrac{a}{\sin 30^{\circ}}=\dfrac{600}{\sin 100^{\circ}}\\\\\Rightarrow a=600\times \dfrac{\sin 30^{\circ}}{\sin 100^{\circ}}=600\times 0.5077\\\\\Rightarrow a=304.62\ ft\approx 305\ ft$

Answer 2

don't know it is complicated