If Tom Bombadil's house is 12 miles east of Hobbiton and 16 miles south, what is the straight line distance (omit units)
Where do I start ?
Put Hobbinton at the origin (0,0) on the x-y grid
then Tom's house would be (12,-16)
distance from (0,0) to (12,-16)
= √(12^2 + (-16)^2)
= √400
= 20
Well, you might want to start by putting on your walking shoes and gathering snacks for the journey. And don't forget a compass in case you veer off course and end up in Mordor! But to answer your question, to find the straight line distance between Tom Bombadil's house and Hobbiton, you could use the Pythagorean theorem. So, grab your trusty hobbit-sized calculator and get ready for some math!
To find the straight-line distance between two points in a coordinate plane, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the distance from Tom Bombadil's house to Hobbiton as the two sides of a right triangle, with 12 miles as the vertical side and 16 miles as the horizontal side.
To find this distance, you can follow these steps:
1. Square the length of the vertical side (12 miles) and the length of the horizontal side (16 miles).
Vertical side squared = (12 * 12) = 144
Horizontal side squared = (16 * 16) = 256
2. Add the squared values together.
144 + 256 = 400
3. Take the square root of the sum to find the straight-line distance.
√400 = 20
Therefore, the straight-line distance between Tom Bombadil's house and Hobbiton is 20 (omit units).
To find the straight line distance between Tom Bombadil's house and Hobbiton, you can use the Pythagorean theorem. This theorem states that in a right-angled 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 other two sides.
In this case, you can consider the distance from Hobbiton to Tom Bombadil's house as the two sides of a right-angled triangle, with the straight line distance being the hypotenuse.
To start solving the problem:
1. Draw a diagram representing the situation, with Hobbiton and Tom Bombadil's house as points. Label the distance from Hobbiton to Tom Bombadil's house as the two sides of the right-angled triangle.
2. Use the Pythagorean theorem to find the length of the straight line distance. The formula is: c^(2) = a^(2) + b^(2), where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
3. Substitute the given values into the formula. In this case, a = 12 miles (east) and b = 16 miles (south).
4. Calculate the square of each side: a^(2) = 12^(2) = 144 and b^(2) = 16^(2) = 256.
5. Add the squares of the sides: 144 + 256 = 400.
6. Take the square root of the sum to find the length of the hypotenuse: sqrt(400) = 20.
Therefore, the straight line distance between Tom Bombadil's house and Hobbiton is 20 miles.