Question

You own a summer home on the east side of Lake George in New York's Adirondack Mountains. To drive to your favorite restaurant on the west side of the lake, you must go directly south for 7 miles and then directly west for 3 miles. If you could go directly to the restaurant in your boat, how long would the boat trip be?

Short answer

Answer: The distance between the summer home and the favorite restaurant is approximately 7.62 miles when traveled directly by boat.

Step-by-step solution

Identify the given sides of the right-angled triangle

The given sides of the triangle are: a = 7 miles (southward distance) b = 3 miles (westward distance)

Use the Pythagorean theorem to find the length of the direct boat trip

The Pythagorean theorem states that for any right-angled triangle: a^2 + b^2 = c^2 We can plug in the values for a and b into the formula: (7^2) + (3^2) = c^2 49 + 9 = c^2 58 = c^2

Solve for the length of the boat trip (c)

To find the value of c, take the square root of both sides of the equation: sqrt(58) = c c ≈ 7.62 miles So, the length of the direct boat trip to the restaurant is approximately 7.62 miles.