A pole which is 9 m long is placed against the wall. If the foot of the pole is 7 m away from the wall, how high is the top of the pole from the ground? Give non-exact numerical answers correct to 3 significant figures.

This problem can be solved using the Pythagorean theorem, which 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.

Here, the pole is the hypotenuse of a right triangle, the distance from the foot of the pole to the wall is one side of the triangle, and the height from the ground to the top of the pole is the other side.

1. Identify the lengths of the sides of the triangle. The hypotenuse (pole) is 9 m long, and one side (distance from the wall) is 7 m long.

2. Use the Pythagorean theorem to find the length of the other side (height of the pole). The formula is a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

3. Substitute the known values into the formula: 7² + b² = 9².

4. Simplify the equation: 49 + b² = 81.

5. Solve for b²: b² = 81 - 49 = 32.

6. Find the square root of 32 to get the length of b (height of the pole). The square root of 32 is approximately 5.657.

So, the top of the pole is approximately 5.657 m from the ground, to three significant figures.