The image provides a trigonometric problem where the length of the shadow of a building is 57 feet, and the angle of elevation of the sun is 55°. We are tasked with finding the height of the building.

This situation forms a right triangle, where:

• The angle of elevation (θ) is 55°.
• The adjacent side (shadow length) is 57 feet.
• The opposite side (height of the building) is what we need to find.

We can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substituting the known values:

$\tan(55^\circ) = \frac{h}{57}$

To find the height $h$:

$h = 57 \times \tan(55^\circ)$

Let's calculate the height.The height of the building is approximately 81.4 feet, rounded to the nearest tenth.

Do you want further clarification or details on this solution?

Here are some related questions to consider:

1. How would the height change if the angle of elevation was greater?
2. What other trigonometric functions could be used in similar problems?
3. How do we interpret the tangent function in terms of real-world applications like this?
4. What would happen to the height if the shadow length was shorter?
5. How can we verify this calculation using another method?

Tip: In trigonometric problems, it's essential to ensure your calculator is set to the correct mode (degrees or radians) based on the angle unit being used.