building a and building b are 500 meters apart. there is no road between them, so to drive from building a…

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

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

Answer

Explanation:

Step1: Find the lengths of the sides of the right - triangle

In right - triangle ABC, given the hypotenuse (AB = 500) meters and (\angle B=60^{\circ}). We know that (\cos B=\frac{BC}{AB}) and (\sin B=\frac{AC}{AB}). Since (\cos60^{\circ}=\frac{1}{2}), then (BC = AB\times\cos60^{\circ}=500\times\frac{1}{2}=250) meters. Since (\sin60^{\circ}=\frac{\sqrt{3}}{2}), then (AC = AB\times\sin60^{\circ}=500\times\frac{\sqrt{3}}{2}=250\sqrt{3}\approx250\times1.732 = 433) meters.

Step2: Calculate the driving distance and the walking distance

The walking distance from A to B is (d_{walk}=500) meters. The driving distance from A to B via C is (d_{drive}=AC + BC=433+250 = 683) meters.

Step3: Calculate the difference

The difference (\Delta d=d_{drive}-d_{walk}=683 - 500=183) meters.

Answer:

183 meters