Final answer:
The original question does not provide sufficient information to calculate the height of the mountain peak. Heights can be calculated using trigonometric methods or by analyzing photographs. Mount Everest at 29,029 feet is approximately 8.848 kilometers high.
"The correct option is approximately option b"
Step-by-step explanation:
The question as stated does not provide enough information to determine the height of the peak being viewed by the surveyor. Typically, determining the height of a mountain peak requires additional data, such as the distance to the peak, the angle of elevation to the top of the peak, or the use of trigonometric methods if the base and the angle to the peak are known.
However, we can discuss how the height of a mountain can be measured. One way is using trigonometry if the surveyor measures the angle of elevation from a known distance from the base of the peak. Using the tangent of the angle and the distance to the mountain, the height can be calculated. For example, if a mountain is 10 km away and the angle of elevation to the peak is measured to be 15 degrees, the height of the mountain would be the tan(15°) multiplied by the distance to the mountain.
Additionally, if the height of a mountain or cliff is known and a photograph is taken using a telephoto lens with a known focal length, the image properties can be analyzed to infer distances or scales. For instance, if a 200 mm focal length lens is used to photograph a 1000 m high cliff from 10.0 km away, the height of the image on the film (or sensor) can be calculated using principles of optics.
The height of Mount Everest often serves as a reference point for these sorts of questions. Mount Everest, which is 29,029 feet tall, is about 8.848 kilometers high when converted from feet using the conversion factor of 1 kilometer equals 3,281 feet. This value is based on the height above sea level, which is the standard for measuring the heights of mountains.