To solve this problem, we can 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. This can be written as: a² + b² = c².

Here, the distance Shane drives north can be one side of the triangle (a = 3 miles), the distance he drives east can be the second side (b = 5 miles), and the straight-line distance between his parents' and grandparents' houses is the hypotenuse we're solving for (c).

Substituting the given values into the Pythagorean theorem gives us:

3² + 5² = c²
9 + 25 = c²
34 = c²

To solve for c, we take the square root of both sides:

c = sqrt(34) ≈ 5.8 miles

So, the straight-line distance between Shane's parents' and grandparents' houses is approximately 5.8 miles.

Question

To solve this problem, we can 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. This can be written as: a² + b² = c².

Here, the distance Shane drives north can be one side of the triangle (a = 3 miles), the distance he drives east can be the second side (b = 5 miles), and the straight-line distance between his parents' and grandparents' houses is the hypotenuse we're solving for (c).

Substituting the given values into the Pythagorean theorem gives us:

3² + 5² = c²
9 + 25 = c²
34 = c²

To solve for c, we take the square root of both sides:

c = sqrt(34) ≈ 5.8 miles

So, the straight-line distance between Shane's parents' and grandparents' houses is approximately 5.8 miles.

Knowee AI · Accepted Answer

To solve this problem, we can 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. This can be written as: a² + b² = c².

Here, the distance Shane drives north can be one side of the triangle (a = 3 miles), the distance he drives east can be the second side (b = 5 miles), and the straight-line distance between his parents' and grandparents' houses is the hypotenuse we're solving for (c).

Substituting the given values into the Pythagorean theorem gives us:

3² + 5² = c²
9 + 25 = c²
34 = c²

To solve for c, we take the square root of both sides:

c = sqrt(34) ≈ 5.8 miles

So, the straight-line distance between Shane's parents' and grandparents' houses is approximately 5.8 miles.

To get to his parents' house, Shane would have to drive due north 3 miles. To get to his grandparents' house, he would have to drive due east 5 miles. What is the straight-line distance between the parents' and grandparents' houses? If necessary, round to the nearest tenth.

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