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Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins 4545 inches from the block and the block is 2828 inches tall, how long is the piece of wood? \newline_____ inches

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Full solution

Q. Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins 4545 inches from the block and the block is 2828 inches tall, how long is the piece of wood? \newline_____ inches
  1. Identify Triangle Formed: Identify the right triangle formed by the ramp, ground, and height of the block. The ground is one leg, the height of the block is the other leg, and the piece of wood is the hypotenuse.
  2. Measurements of Triangle: Ground distance (leg 11): 4545 inches, Height of block (leg 22): 2828 inches, Length of wood (hypotenuse): xx inches.
  3. Apply Pythagorean Theorem: Use the Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the legs and cc is the hypotenuse.
  4. Plug in Values: Plug in the values: 452+282=x245^2 + 28^2 = x^2.
  5. Calculate Squares: Calculate the squares: 2025+784=x22025 + 784 = x^2.
  6. Add Squares: Add the squares: 2025+784=28092025 + 784 = 2809.
  7. Find Square Root: Find the square root of 28092809 to solve for xx: 2809=x\sqrt{2809} = x.
  8. Calculate Final Value: Calculate the square root: x=53x = \sqrt{53}.

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