# 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.

January 30, 2021 | education

| **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.