Two pines grow 32 m from one another. One is 37 m high and the other 13 m.

Two pines grow 32 m from one another. One is 37 m high and the other 13 m. Find the distance in meters between their tops.

The figure formed by two pines is a rectangular trapezoid ABCD with bases AB = 37 cm, CD = 13 m. The distance between the tops of the pines (C and B) is the large side of the trapezoid.

Let’s draw the height of the CH trapezoid. Since CDAH is a rectangle, then AH = CD = 13 m, then BH = AB – AH = 37 – 13 = 24 m.

Then, in a right-angled triangle ВСН, according to the Pythagorean theorem, we determine the length of the hypotenuse ВС.

BC ^ 2 = BH ^ 2 + CH ^ 2 = 24 ^ 2 + 32 ^ 2 = 576 + 1024 = 1600.

BC = 40 m.

Answer: The distance between the tops of the pines is 40 m.