on a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and the shadow is 32 meters, how tall is the flag pole

We can solve this problem using the Pythagorean theorem, which states:

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

where:
- \(a\) is the height of the flagpole,
- \(b\) is the length of the shadow (32 meters),
- \(c\) is the hypotenuse (40 meters).

We need to find the height of the flagpole (\(a\)).

Plugging the values into the equation:

\[
a^2 + 32^2 = 40^2
\]

\[
a^2 + 1024 = 1600
\]

Subtract 1024 from both sides:

\[
a^2 = 1600 - 1024
\]

\[
a^2 = 576
\]

Now, take the square root of both sides:

\[
a = \sqrt{576} = 24
\]

Thus, the height of the flagpole is **24 meters**.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How would the height of the flagpole change if the shadow length increased?
2. Can you apply the Pythagorean theorem to find the height if the shadow is unknown but the height and hypotenuse are given?
3. What would happen to the height if the hypotenuse were shorter?
4. How do you calculate the angle of elevation of the sun in this scenario?
5. Can trigonometry be used to find the height without using the Pythagorean theorem?

**Tip**: Always label the sides of a triangle carefully when applying the Pythagorean theorem!

On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 meters long and the shadow is 32 meters, how tall is the flag pole?

Solve the problem of finding the height of a flagpole using the Pythagorean Theorem. The flagpole forms a right triangle with its shadow, where the hypotenuse is 40 meters and the shadow is 32 meters long. This detailed solution is suitable for Grades 7-9 students.

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