Math Problem Statement

Closside is 14 km north and 20 km east of Farlisle. Use Pythagoras' theorem to calculate the direct distance between Closside and Farlisle. Give your answer to 1 d.p.

Solution

To calculate the direct distance between Closside and Farlisle using Pythagoras' theorem:

  1. The vertical distance (north-south direction) is 14 km.
  2. The horizontal distance (east-west direction) is 20 km.
  3. These form the two legs of a right triangle, with the hypotenuse being the direct distance we want to find.

Using Pythagoras' theorem: c=a2+b2c = \sqrt{a^2 + b^2} where a=14a = 14, b=20b = 20, and cc is the hypotenuse.

c=142+202c = \sqrt{14^2 + 20^2} c=196+400c = \sqrt{196 + 400} c=596c = \sqrt{596} c24.4km (rounded to 1 decimal place).c \approx 24.4 \, \text{km (rounded to 1 decimal place)}.

The direct distance between Closside and Farlisle is approximately 24.4 km.


Do you want further details or have any questions?
Here are 5 related questions to expand your understanding:

  1. How can we use Pythagoras' theorem in real-world navigation problems?
  2. What are other applications of Pythagoras' theorem in physics or engineering?
  3. How do we verify the accuracy of calculations involving square roots?
  4. What happens if the distances given are not orthogonal? How do we adapt the calculation?
  5. What would be the result if either distance (14 km or 20 km) were doubled?

Tip: Always double-check unit consistency in your calculations to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Square Roots

Formulas

c = √(a² + b²)

Theorems

Pythagoras' Theorem

Suitable Grade Level

Grades 6-8