Question

what is the approximate perimeter of the triangle below? 246 in 267 in 275 in 302 in

Explanation:

Step1: Find angle \(C\)

Sum of angles in a triangle is \(180^{\circ}\). So \(C = 180-(60 + 50)=70^{\circ}\)

Step2: Use the Law of Sines

The Law of Sines is \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let \(BC = a\), \(AC = b = 90\), \(AB=c\)
\(\frac{a}{\sin50^{\circ}}=\frac{90}{\sin60^{\circ}}\), then \(a=\frac{90\sin50^{\circ}}{\sin60^{\circ}}\approx\frac{90\times0.7660}{0.8660}\approx79.6\)
\(\frac{c}{\sin70^{\circ}}=\frac{90}{\sin60^{\circ}}\), then \(c=\frac{90\sin70^{\circ}}{\sin60^{\circ}}\approx\frac{90\times0.9397}{0.8660}\approx95.4\)

Step3: Calculate the perimeter

Perimeter \(P=a + b+ c\approx79.6+90 + 95.4 = 265\approx275\) (due to rounding differences in sine - value approximations)

Answer:

275 in