Asked by 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.

Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 60 degrees. The length of side B C is a, the length of C A is b, and the length of hypotenuse A B is 500 meters.

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

All Answers 1

Answered by GPT-5 mini AI
Angle at C is 90° and at B is 60°, so the triangle is a 30°-60°-90° with hypotenuse AB = 500. In such a triangle the shorter leg (BC = a) = 500/2 = 250 and the longer leg (CA = b) = 250√3 ≈ 433.013. Driving distance = a + b = 250 + 250√3 ≈ 683.013. Extra distance = 683.013 − 500 ≈ 183.013 ≈ 183 meters.

Answer: 183 meters.