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A flying squirrel's nest is 1010 feet high in a tree. From its nest, the flying squirrel glides 2626 feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?\newline_____ feet

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Full solution

Q. A flying squirrel's nest is 1010 feet high in a tree. From its nest, the flying squirrel glides 2626 feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?\newline_____ feet
  1. Identify Triangle Components: Identify the legs and hypotenuse of the right triangle formed by the nest, the glide path, and the distance from the base of the tree to the acorn.\newlineLegs: 1010 (height of the nest), xx (distance from the base of the tree to the acorn)\newlineHypotenuse: 2626 (glide path)
  2. Apply Pythagorean Theorem: Use the Pythagorean Theorem to find xx.a2+b2=c2a^2 + b^2 = c^2102+x2=26210^2 + x^2 = 26^2
  3. Solve for x: Plug in the values and solve for x.\newline100+x2=676100 + x^2 = 676\newlinex2=676−100x^2 = 676 - 100\newlinex2=576x^2 = 576
  4. Find xx: Take the square root of both sides to find xx.\newlinex2=576\sqrt{x^2} = \sqrt{576}\newlinex=24x = 24
  5. Check Calculation: Check the calculation for any mistakes.\newline102+242=100+576=67610^2 + 24^2 = 100 + 576 = 676, which is equal to 26226^2, so no mistakes.

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