The problem asks to find the height $h$ of a right triangle based on the given angles and the length of the base. Let's break down the information in the image:

• Angle near the base: $29.5^\circ$
• Angle at the top: $49.2^\circ$
• Base (adjacent to both angles): 392 ft
• The triangle is a right triangle.

Since we know the base and the angles, we can use trigonometric ratios to find the height $h$.

The relation between the height $h$ (opposite to the $49.2^\circ$ angle) and the base is given by the tangent function:

$\tan(49.2^\circ) = \frac{h}{392}$

Solving for $h$:

$h = 392 \times \tan(49.2^\circ)$

Let me calculate the value.The height $h$ is approximately 454.14 feet.

Would you like further details or explanations on this solution? Here are five related questions you could explore:

1. How would you solve for the height using the angle $29.5^\circ$ instead of $49.2^\circ$?
2. What if the base was 500 feet instead of 392 feet—how would that affect the height?
3. How can the Pythagorean theorem be applied to this triangle?
4. How do sine and cosine functions relate to this triangle?
5. What other methods can be used to solve for the height in different types of triangles?

Tip: Remember that trigonometric functions are very useful for solving problems involving right triangles when angles and sides are known.