Question

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

Answer 1

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

Answer 2

`\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!