Question

(4 pts) Henry walks out of his hall and proceeds to walk 200 feet due north. He then turns left (west) and walks 190 more feet. Finally, he turns 45∘ left and walks 260 feet. How many feet is Henry from his starting point

Answer 1

Henry is approximately 276 feet from his starting point.

Explanation:

To find how many feet Henry is from his starting point, you can use the Pythagorean theorem because he walked in both the north and west directions, creating a right triangle. Here's the calculation:

1. The distance he walked north is 200 feet.

2. The distance he walked west is 190 feet.

3. The 45-degree angle forms a right triangle.

Now, use the Pythagorean theorem:

a² + b² = c²

Where:

a = 200 feet (north)

b = 190 feet (west)

a² + b² = c²

(200)² + (190)² = c²

40000 + 36100 = c²

76100 = c²

Now, find the square root of 76100:

c = √76100 ≈ 276 feet

So, Henry is approximately 276 feet from his starting point.