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

Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

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

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