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

183 m

Step-by-step explanation:

See the attached figure....

Find the distance BC. We know that in the right triangle ABC

Cos(60°) = BC/AB ----> adjacent side divided by the hypotenuse

Remember that

Cos (60°) = 1/2

substitute the values

1/2 = a / 500

a = 250 m

step 2

Find the distance AC

In the right triangle ABC

Sin (60°) = AC/AB----> opposite side divided by the hypotenuse

Remember that

Sin(60°) = √3/2

substitute the values

√3/2 = b/500

b = 250√3 = 433 m

step 3

Find the distance AC+CB

433 + 250 = 683 m

Subtract the distance AB from 683 m

683 - 500 = 183 m

a² + b²= c²

24² + 7² = c²

c= 25