The length of the sun’s shadow from the tree is 24 m, a vertical pole 1.5 m high casts a shadow of 1.6.

The length of the sun’s shadow from the tree is 24 m, a vertical pole 1.5 m high casts a shadow of 1.6. Find the height of the trees

If you connect the top of the tree with the end of the tree shadow and the top of the pole with the end of its shadow, you get two right-angled triangles. One angle for them is 90 °, and the angles that form the hypotenuse of these triangles with the Earth’s surface are equal, therefore, these triangles are similar, which means that their sides are proportional.

Let’s make a proportion that describes the ratio of the sides of the triangles:

1.6 m – 1.5 m;

24 m – x m.

Let’s solve this proportion:

x = 24 * 1.5: 1.6 = 22.5 m tree height.

Answer: the height of the tree is 22.5 m.