A boat sails due east for 10km the sails north for 5km. How far in km is the boat from starting position?*A. 3√3B. 3√5C. 5√3D. 10√3
Question
A boat sails due east for 10km the sails north for 5km. How far in km is the boat from starting position?*A. 3√3B. 3√5C. 5√3D. 10√3
Solution
The problem describes a right triangle where the boat's eastward journey forms one leg (10 km), the northward journey forms the second leg (5 km), and the distance from the starting position (which we're trying to find) is the hypotenuse.
We can use the Pythagorean theorem to solve this, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). It's usually written as: a² + b² = c².
Here, a = 10 km (eastward journey), b = 5 km (northward journey), and c is the distance from the starting position.
So, we substitute a and b into the Pythagorean theorem:
(10 km)² + (5 km)² = c² 100 km² + 25 km² = c² 125 km² = c²
To solve for c, we take the square root of both sides:
c = √125 km c = 5√5 km
So, the boat is 5√5 km from the starting position. The correct answer is B. 5√5.
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