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Towns A and C are connected bya straight highway which is 60 miles long . The straight line distance between A and town B is 50 miles , and the striahgt line distnace from town B to town C is 50 miles . How many miles is it from town B to the point on the highway connecting towns A and C which is closest to town B?

Towns A and C are connected bya straight highway which is 60 miles long . The straight line distance between A and town B is 50 miles , and the striahgt line distnace from town B to town C is 50 miles . How many miles is it from town B to the point on the highway connecting towns A and C which is closest to town B?

30 40 50 30sqrt2 60

height of the traingle ABC (corresponding to point B) = (BC^2 - (AC/2)^2)^1/2 = (50^2 - 30^2)^1/2 = 40.

Quickest way without solving is to have ABC in a right triangle. BC and BA are the two sides = 50 with AC the hypotenuse = 60. Cut across from B to AC dividing the hypotenuse in half = 30. Call this point T. The new triangle ATB is in the 3:4:5 ratio or 30:40:50.

Quickest way without solving is to have ABC in a right triangle. BC and BA are the two sides = 50 with AC the hypotenuse = 60. Cut across from B to AC dividing the hypotenuse in half = 30. Call this point T. The new triangle ATB is in the 3:4:5 ratio or 30:40:50.

Bravo, ndidi204! 3:4:5, 5:12:13 are widely known Pifagorian numbers.

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