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 length of side $a$

$\cos(60^\circ) = \frac{a}{500} \implies a = 500 \times \cos(60^\circ) = 500 \times 0.5 = 250$ meters

Step2: Find length of side $b$

$\sin(60^\circ) = \frac{b}{500} \implies b = 500 \times \sin(60^\circ) = 500 \times \frac{\sqrt{3}}{2} \approx 433.01$ meters

Step3: Calculate driving distance

$a + b = 250 + 433.01 = 683.01$ meters

Step4: Find difference in distances

$683.01 - 500 = 183.01$ meters

Step5: Round to nearest whole number

$183.01 \approx 183$ meters

Answer:

183 meters