Question

9) Show your work for how you found the distance between the School →
Fire Station. Be sure to include ALL steps necessary. school to fire station is Aside is 90 yards and B side 30 yards

Answer 1

To find the distance between the school and the fire station using the given sides, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The formula is:

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

Where:
- \(c\) is the length of the hypotenuse,
- \(a\) and \(b\) are the lengths of the other two sides.

In this case, you have:
- \(a = 90\) yards (one side),
- \(b = 30\) yards (the other side).

### Step 1: Square the lengths of sides a and b.
\[
a^2 = 90^2 = 8100 \text{ yards}^2
\]
\[
b^2 = 30^2 = 900 \text{ yards}^2
\]

### Step 2: Add the squares of a and b.
\[
a^2 + b^2 = 8100 + 900 = 9000 \text{ yards}^2
\]

### Step 3: Take the square root to find c (the distance between the school and the fire station).
\[
c = \sqrt{9000}
\]

### Step 4: Calculate the square root.
\[
c \approx 94.868 \text{ yards}
\]

Therefore, the distance between the school and the fire station is approximately 94.87 yards.