Distance calculation (right triangle)

In summary, the distance between city A and city D is 540.8 miles. The offered answers of 300, 400, 500, and 600 miles are most likely incorrect due to a mistake in rounding or significant figures. The correct answer should be 500 miles, taking into consideration the 2 significant figures in 300 and 700.
  • #1
future_vet
169
0

Homework Statement


Starting from city A, a car drives 250 miles east to city B, then 300 miles north to city C, and then 700 miles west to city D. What is the distance between city A and city D? (Points: 1)
300 mi
400 mi
500 mi
600 mi

Homework Equations


A^2 + B^2 = C^2

The Attempt at a Solution



A^2= 300^2
B^2= (700-250)^2
C^2= 292500
C= 540.8 miles.
Which answer should I choose? 500 or 600?

Thanks!
 
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  • #2
Are you sure these are the listed answers?
 
  • #3
Yes, did you get the same result I did?... Maybe it has something to do with significant figures?...
 
  • #4
future_vet said:
Yes, did you get the same result I did?... Maybe it has something to do with significant figures?...

Your calculation is correct. The offered answers are obviously wrong. Mistakes happen. :wink:
 
  • #5
I will ask the professor.
Thanks anyway!
 
  • #6
I think that the answer is 500. He might count 300 and 700 to only have 2 significant figures, as opposed to 300. and 700. which have 3. Therefore, if the answer is 540, it would only be 500 if we take this into consideration... I think.
 

1. How do you calculate the distance in a right triangle?

The distance in a right triangle can be calculated using the Pythagorean theorem, which states that 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 other words, distance = √(a² + b²), where a and b are the lengths of the other two sides.

2. What is the purpose of calculating distance in a right triangle?

The purpose of calculating distance in a right triangle is to find the length of the hypotenuse, which is often used in various mathematical and scientific applications. It can also be used to find the distance between two points in a coordinate plane.

3. What units should be used when calculating distance in a right triangle?

The units used for distance calculation in a right triangle should be consistent with the units used for the given side lengths. For example, if the side lengths are given in meters, the distance would also be in meters.

4. Can the Pythagorean theorem be used in non-right triangles?

No, the Pythagorean theorem can only be used in right triangles, where one of the angles is a right angle (90 degrees). It cannot be applied to non-right triangles, as they have different formulas for calculating distance.

5. How accurate is distance calculation in a right triangle?

The accuracy of distance calculation in a right triangle depends on the accuracy of the given side lengths. If the side lengths are measured or estimated with high precision, the calculated distance will also be accurate. However, if there are errors in the side lengths, the calculated distance will also be affected.

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