Question

The altitude of a mountain peak is measured as shown in the figure to the right. At an altitude of 14,514 feet on a different mountain, the straight-line distance to the peak of Mountain A is 27.8058 miles and the peak's angle of elevation is θ=5.5900°. (a) Approximate the height (in feet) of Mountain A.(b) In the actual measurement, Mountain A was over 100 mi away and the curvature of Earth had to be taken into account. Would the curvature of Earth make the peak appear taller or shorter than it actually is?

Answer 1

Answer:

a. 14,516.7086

b. shorter

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`
`\sin 5.5900=\frac{\text{opposite}}{27.8059}`
`\text{opposite}=2.7086`

To get the approximate height of Mountain A, we will add the height that we got earlier to 14,514 ft.

`14,514+2.7086=14516.7086ft`

b.) Since the distance is over 100 miles away, this would create an effect that will make the peak appear shorter than it actually is.