A tree 8 m tall casts a shadow 15 m long on the ground. Find the distance between

the top of the tree and the end of its shadow.

O 23 m

O 12.7 m

O 7m

O

17 m

The distance from the top of the tree to the end of its shadow is 17 m ⇒ 4th answer

Step-by-step explanation:

The relation between the three sides a, b and c of a right triangle, where c is the hypotenuse and b, c are the legs of the right angle is:

c² = a² + b² ⇒ Pythagoras Theorem

The tall of the tree (T) and its shadow in the ground (S) form two legs of a right triangle and the distance from the top of the tree to the end of the shadow (D) formed the hypotenuse of the triangle

By using Pythagoras Theorem

∵ (D) ² = (T) ² + (S) ²

∵ The tree is 8 m tall

∴ T = 8

∵ It casts a shadow 15 m long on the ground

∴ S = 15

- Substitute them in the formula above

∴ (D) ² = (8) ² + (15) ²

∴ (D) ² = 64 + 225

∴ (D) ² = 289

- Take √ for both sides

∴ D = 17

The distance from the top of the tree to the end of its shadow is 17 m