To solve the problem, we can observe that the scenario forms a right triangle. The height of the building (29 m) is one leg of the triangle, the length of the shadow is the other leg, and the hypotenuse is the distance from the top of the building to the tip of the shadow (35 m).

We can apply the Pythagorean theorem to find the length of the shadow. The theorem states:

$a^2 + b^2 = c^2$

Where:

• $a$ is the height of the building (29 m),
• $b$ is the unknown length of the shadow,
• $c$ is the hypotenuse (35 m).

Let's solve for $b$ (the length of the shadow):

$29^2 + b^2 = 35^2$

$841 + b^2 = 1225$

$b^2 = 1225 - 841$

$b^2 = 384$

$b = \sqrt{384}$

$b \approx 19.6 \, \text{m}$

So, the length of the shadow is approximately 19.6 meters, rounded to the nearest tenth.

Would you like further clarification on any part of the solution, or more details?

Here are 5 related questions for further exploration:

1. How would the problem change if the height of the building were different?
2. Can you solve for the angle of elevation of the sun in this scenario?
3. How does the length of the shadow change with the sun's position in the sky?
4. What would happen if we rounded the answer to the nearest hundredth instead?
5. How could you use trigonometric ratios to solve this problem?

Tip: The Pythagorean theorem is useful whenever you have a right triangle and need to find the length of one side when the lengths of the other two sides are known.