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Three trees in a park form a right triangle. An ash tree is located at point A, a beech tree at point B, and a cherry tree at point C. The right angle of the triangle is located at point A.

The town plants a dogwood tree at point D, which is at the intersection of the hypotenuse of the right triangle and the altitude from point A. If the distance from the beech tree to the dogwood tree is 60 feet and the distance from the ash tree to the dogwood tree is 110 feet, what is the distance from the beech tree to the cherry tree?

Answer :

To find the distance from the Beech tree to the Cherry tree in a right triangle scenario involving other trees' distances, you can use the Pythagorean theorem with given values to calculate the unknown distance.

Given:

  1. Distance from Beech to Dogwood: 60 feet
  2. Distance from Ash to Dogwood: 110 feet

To find: Distance from Beech to Cherry

Solution:

  1. Using Pythagorean theorem: 56² + 54² = c²
  2. c = √6052 = 78 feet

Therefore, the distance from the Beech tree to the Cherry tree is 78 feet.

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Rewritten by : Jeany

The distance from the beech tree to the cherry tree is 90 feet.

How to find the distance?

This is a classic problem in trigonometry.

Since we know that one angle of the triangle is a right angle, we can use the Pythagorean Theorem to solve for the length of the hypotenuse.

If we let the distance from the ash tree to the cherry tree be x, we know that:

x^2 + 110^2 = 60^2

Solving for x, we get:

x = sqrt(60^2 - 110^2)

x = sqrt(3600 - 12100)

x = sqrt(-8500)

x = sqrt(8500)

x = 90


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