Find the height of a tree if the length of its shadow is 8.4 meters, and the length of the shadow

Find the height of a tree if the length of its shadow is 8.4 meters, and the length of the shadow from a vertical pillar 2 meters high at the same time of day is 2.4 meters.

1. Let’s designate the height of the tree AB, its shadow AC. We connect point B with point C. We got

right-angled triangle triangle ABC.

AC = 8.4 m.

2. Let’s designate the height of the pillar MK, its shadow ME. We connect point K with point E. Received a right-angled triangle MKE triangle.

MK = 2 m. ME = 2.4 m.

3. ∠В = 90 °, since the tree grows vertically, perpendicular to the surface of the earth and, accordingly, a straight AC.

4. ∠М = 90 °, since the pillar is installed vertically perpendicular to the surface of the earth and, accordingly, straight line ME.

5. ∠С = ∠Е, since the rays of the sun fall at the same angle.

6. In the above triangles, two angles are equal. Therefore, triangles ABC and MKE are similar.

7. Let’s make the proportion:

AB: MK = AC: ME.

AB = MK x AC / ME = 2 x 8.4 / 2.4 = 7 m.

Answer: the height of the tree is 7 meters.