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A boat leaves crab island searching for treasure and goes 1212 miles south, then turns and goes east for 1616 miles. How far away is the boat from where it started?

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Full solution

Q. A boat leaves crab island searching for treasure and goes 1212 miles south, then turns and goes east for 1616 miles. How far away is the boat from where it started?
  1. Identify Problem: Identify the problem and set up the scenario.\newlineThe boat travels in a straight line south and then east, forming a right triangle with the path south as one leg and the path east as the other leg. The distance from the starting point to the boat's current position is the hypotenuse of this triangle.\newlineCalculation: South leg = 1212 miles, East leg = 1616 miles.
  2. Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the hypotenuse.\newlineUsing the formula for the Pythagorean Theorem, a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the legs of the triangle and cc is the hypotenuse.\newlineCalculation: 122+162=c212^2 + 16^2 = c^2
  3. Calculate Squares: Calculate the squares of the legs.\newlineCalculate 12212^2 and 16216^2.\newlineCalculation: 122=14412^2 = 144, 162=25616^2 = 256
  4. Add Squares: Add the squares of the legs to find c2c^2.\newlineAdd the results from the previous step.\newlineCalculation: 144+256=400144 + 256 = 400
  5. Solve for Distance: Solve for cc by taking the square root of c2c^2.\newlineFind the square root of 400400 to get the distance.\newlineCalculation: c=400=20c = \sqrt{400} = 20

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