Answer:
To solve this problem, we can use the trigonometric relationship between the angle of elevation, the distance from the observation point to the base of the geyser, and the height of the geyser.
Given information:
- Observation point is 20 feet from the base of the geyser.
- The angle of elevation to the top of the geyser is 50°.
Let's denote the height of the geyser as "h".
We can use the tangent ratio to find the height of the geyser:
tan(θ) = opposite / adjacent
tan(50°) = h / 20
Solving for h:
h = tan(50°) × 20
h = 23.94 feet
Therefore, the height of the geyser is approximately 23.94 feet.