The distance between A and C is 60 miles and the distance between A and B is 50 miles and the distance between B and C is 50 miles. What is the distance from B to the straight line between A and C?

Answer 1

Draw an isosceles triangle with a base A-C of length 60. The apex of the triangle, point B, is length 50 from both point A and point C. That's your triangle. Drop a "vertical" from B to the base - where it will form a right angle with that line segment and, because the sides are the same length, will bisect the base. That's the line segment you're looking to find the length of. So let's. The base, length 60, is divided into two equal segments by the vertical. That's two length-30 pieces. Notice that your figure, the isosceles triangle with that vertical drawn in, is two "back-to-back" right triangles, each with a base of length 30 and a hypotenuse of length 50. We can "cheat" here and see that the triangles have sides of length 30, 40 and 50. We also know that 3, 4, 5 is a "magic" right triangle because 32 + 42 = 52 (9 + 16 = 25). Our triangle in this problem has sides (conveniently) ten times the length of the 3, 4, 5 triangle. That makes them 30, 40 and 50 in length. The height of the triangle is 40 miles. If you want to work it through, 302 + h2 = 502 900 + h2 = 2500 h2 = 2500 - 900 = 1600 = 40 Our work checks.