Towns A and C are connected by straight highway which is 60 miles long. The straight-line distance between town A and town B is 50 miles, and the straight-line distance 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?
We have towns A, B, and C, with a straight highway connecting towns A and C, which is 60 miles long. The straight-line distance from A to B is 50 miles, and the straight-line distance from B to C is 50 miles.
The highway connecting A and C can be thought of as the hypotenuse of a right triangle, where the legs of the triangle are the distances from A to B and from B to the point on the highway (let's call it point D).
The triangle formed by points A, B, and D is similar to the triangle formed by points A, B, and C because they share the same angles. This is because vertical angles (formed by the highway and the straight-line distances) are congruent.
We can set up a proportion to find the distance from B to D:
=
Substituting the given values:
= (50 miles is half of 100 miles)
Now, solving for BD:
BD = 30 miles
So, the distance from town B to the point on the highway connecting towns A and C, which is closest to town B, is 30 miles.
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