Question

building a and building b are 500 meters apart. there is no road between them, so to drive from building a to building b, it is necessary to first drive to building c and then to building b. about how much farther is it to drive than to walk directly from building a to building b? round to the nearest whole number. 183 meters 250 meters 366 meters 683 meters

Explanation:

Step1: Find the length of \(a\) and \(b\)

Using trigonometric ratios in right - triangle \(ABC\) with \(\angle B = 60^{\circ}\) and hypotenuse \(AB = 500\) m.
For \(a\) (adjacent side to \(\angle B\)): \(\cos60^{\circ}=\frac{a}{500}\), so \(a = 500\times\cos60^{\circ}=500\times0.5 = 250\) m.
For \(b\) (opposite side to \(\angle B\)): \(\sin60^{\circ}=\frac{b}{500}\), so \(b = 500\times\sin60^{\circ}=500\times\frac{\sqrt{3}}{2}\approx500\times0.866 = 433\) m.

Step2: Calculate the driving distance and the difference

The driving distance is \(a + b=250 + 433=683\) m.
The walking distance is \(500\) m.
The difference is \(683−500 = 183\) m.

Answer:

183 meters