For a physics experiment, a ramp is built from a board that is 7.25 m long. If the ramp will have a vertical height of 5.30 m, what will be the horizontal length of the ramp to the nearest hundredths of a meter? (2 decimal places)
Question
For a physics experiment, a ramp is built from a board that is 7.25 m long. If the ramp will have a vertical height of 5.30 m, what will be the horizontal length of the ramp to the nearest hundredths of a meter? (2 decimal places)
Solution
To solve this problem, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the board is the hypotenuse (c), the vertical height of the ramp is one side (a), and the horizontal length of the ramp is the other side (b) that we are trying to find.
The Pythagorean theorem is: a² + b² = c²
We know a = 5.30 m and c = 7.25 m. We can substitute these values into the equation and solve for b:
(5.30 m)² + b² = (7.25 m)²
28.09 m² + b² = 52.5625 m²
Subtract 28.09 m² from both sides to isolate b²:
b² = 52.5625 m² - 28.09 m²
b² = 24.4725 m²
Finally, take the square root of both sides to solve for b:
b = √24.4725 m²
b = 4.95 m
So, the horizontal length of the ramp to the nearest hundredths of a meter is 4.95 m.
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