Answer: Certainly! The formula to find the length of the shadow (\(s\)) using the height of an object (\(h\)) and the angle of elevation (\(\theta\)) is given by:
\[ s = \frac{h}{\tan(\theta)} \]
In this case, the height of the building (\(h\)) is 32 meters, and the distance from the top of the building to the tip of the shadow (\(d\)) is 34 meters.
The angle of elevation (\(\theta\)) can be calculated using the arctangent function:
\[ \theta = \arctan\left(\frac{h}{d}\right) \]
Substituting the given values:
\[ \theta = \arctan\left(\frac{32}{34}\right) \]
Once the angle of elevation is found, it can be used in the formula for the length of the shadow:
\[ s = \frac{h}{\tan(\theta)} \]
Substituting \(h = 32\) and \(\theta\) from the previous calculation:
\[ s \approx \frac{32}{\tan(\arctan(32/34))} \]
By evaluating this expression, the length of the shadow is approximately 15.5 meters.
