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31 votes
31 votes
Point A and B are respectively 20m north and 48m east of point c.find the distance AB

User Novice
by
2.1k points

2 Answers

4 votes
4 votes

Answer: Distance AB = 52 m

Explanation:

Given information

Point A = 20 m north of point C

Point B = 48 m east of point C

Please refer to the attachment below for a graphical understanding

Concept

According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.

Therefore, we can use the Pythagorean theorem to find the distance between points A and B.

Given formula

a² + b² = c²

  • a = distance between point A and point C
  • b = distance between point B and point C
  • c = distance between point A and point B

Substitute values into the formula

a² + b² = c²

(20)² + (48)² = c²

Simplify exponents

400 + 2304 = c²

Simplify by addition

2704 = c²

c = √2704

c = 52 or c = -52 (reject, since no distance can be negative)

Therefore, the distance AB is
\Large\boxed{52~m}

Hope this helps!! :)

Please let me know if you have any questions

Point A and B are respectively 20m north and 48m east of point c.find the distance-example-1
User Gomiero
by
3.2k points
18 votes
18 votes

Answer:


\boxed {AB = 52 m}

Explanation:

This forms a right triangle.

Therefore, by using the Pythagorean Theorem, we can find AB.

AB = √AC² + BC²

  • AB = √(20)² + (48)²
  • AB = √400 + 2304
  • AB = √2704
  • AB = 52m

I hope it helped you solve the problem.

Good luck on your studies!

User John Stephens
by
2.7k points
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