You start driving west for 5 miles, turn left, and drive south for another 8 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.

To determine your straight-line distance from the starting point after driving west and then south, we can model the situation as a right triangle. In this scenario, the two legs of the triangle represent the distances traveled west and south, and the hypotenuse represents the straight-line distance from the starting point.

We can use the Pythagorean theorem to find the hypotenuse \( c \):

\[ c^2 = a^2 + b^2 \]

Here:
- \( a = 5 \) miles (west)
- \( b = 8 \) miles (south)

Substituting the values into the equation:

\[ c^2 = 5^2 + 8^2 \]
\[ c^2 = 25 + 64 \]
\[ c^2 = 89 \]
\[ c = \sqrt{89} \]

Calculating the square root of 89:

\[ c \approx 9.433 \]

Rounding to the nearest tenth of a mile:

\[ c \approx 9.4 \]

So, the straight-line distance from your starting point is approximately 9.4 miles.

If you have any questions or need further clarification, feel free to ask. Here are some related questions you might find interesting:

1. How do you use the Pythagorean theorem in navigation?
2. What other real-world scenarios can be modeled using right triangles?
3. How do you calculate distances on a coordinate plane?
4. What are some practical applications of the Pythagorean theorem?
5. Can the Pythagorean theorem be used for non-right triangles?
6. What tools can help in calculating distances in real life?
7. How does GPS technology use geometry to calculate distances?
8. What is the difference between distance and displacement in physics?

**Tip:** When solving problems involving distances, sketching a diagram can help visualize the problem and make calculations easier.

Learn how to calculate the straight-line distance from a starting point after traveling west and south using the Pythagorean theorem. This problem involves a right triangle with legs 5 miles (west) and 8 miles (south). Discover the step-by-step solution and practical applications of the Pythagorean theorem. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation