Question

The diagram below shows the location of landmarks in a local park.

The hypotenuse is 7m

The longest leg is 6 m

the short leg is missing



What is the distance in meters between the flagpole and the statue.

If needed, please round to the nearest tenth.



Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . , -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal.

Answer 1

To find the distance between the flagpole and the statue, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is:

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

In this case, the hypotenuse \( c = 7 \) m, and the longest leg \( a = 6 \) m:

1. Substitute the values into the Pythagorean theorem:

\[
7^2 = 6^2 + b^2
\]

2. Calculate \( 7^2 \) and \( 6^2 \):

\[
49 = 36 + b^2
\]

3. Rearrange to solve for \( b^2 \):

\[
b^2 = 49 - 36
\]

\[
b^2 = 13
\]

4. Take the square root to find \( b \):

\[
b = \sqrt{13}
\]

Calculating \( \sqrt{13} \) gives approximately \( 3.6056 \).

Finally, rounding to the nearest tenth gives:

\[
b \approx 3.6
\]

Thus, the distance between the flagpole and the statue is approximately **3.6** meters.