Three people are sitting on a bus. Leah is seated 8 feet directly behind Joseph and 5 feet directly left of Finn. How far is Joseph from Finn? If necessary, round to the nearest tenth.
Question
Three people are sitting on a bus. Leah is seated 8 feet directly behind Joseph and 5 feet directly left of Finn. How far is Joseph from Finn? If necessary, round to the nearest tenth.
Solution
This problem can be solved using 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.
Here, we can imagine a right triangle where one side is the distance between Leah and Joseph (8 feet), the other side is the distance between Leah and Finn (5 feet), and the hypotenuse is the distance between Joseph and Finn, which we're trying to find.
The Pythagorean theorem formula is a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Substituting the given values into the formula, we get:
8² + 5² = c² 64 + 25 = c² 89 = c²
To find c (the distance between Joseph and Finn), we take the square root of 89, which is approximately 9.4 feet.
So, Joseph is approximately 9.4 feet from Finn.
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