The problem asks to find the height of a building, given the angle of elevation of the sun and the length of the shadow the building casts.

We can use trigonometry to solve this. Specifically, the tangent function relates the angle of elevation to the height of the building and the length of its shadow:

$\tan(\theta) = \frac{\text{height}}{\text{shadow length}}$

Where:

• $\theta = 55.6^\circ$ is the angle of elevation,
• $\text{shadow length} = 36.7$ feet.

The equation becomes:

$\tan(55.6^\circ) = \frac{\text{height}}{36.7}$

Now, solving for the height:

$\text{height} = 36.7 \times \tan(55.6^\circ)$

Let me calculate this.The height of the building is approximately 53.6 feet when rounded to the nearest tenth.

Would you like further details on the calculation or have any questions?

Here are 5 related questions to explore:

1. How would the shadow length change if the angle of elevation were lower?
2. What if the shadow was 50 feet long? How tall would the building be?
3. How do different trigonometric functions relate to the angle of elevation?
4. Can you determine the shadow length if you know the height and the angle?
5. How can we use the sine or cosine functions in similar problems?

Tip: Always ensure your calculator is set to degrees when working with angles in degrees!