Answer: 17,731.15 feet.
Step-by-step explanation:
1. You know that the straight road to the top of a mountain is 25,525 feet long and makes an angle of elevation of 44 degrees from sea level.
2. Therefore, you can draw a right triangle like the is shown in the figure attached, where h is the height and the angle α is the angle of elevation of 44 degrees from sea level.
3. You can calculate the height h as following:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\[/tex]
[tex]\alpha=44[/tex]°
[tex]opposite=h\\hypotenuse=25,525[/tex]
4. Solve for h. Then, you obtain the following result:
[tex]h=25,525*sin(44)\\h=17,731.15[/tex]
