Answer:
The height of the hill is of 9.19 miles.
Step-by-step explanation:
Relations in a right triangle:
The sine of an angle is given by the measure of the opposite side divided by the hypotenuse.
The cosine of an angle is given by the measure of the adjacent side divided by the hypotenuse.
In this question:
Angle of 45º, and drives 13 miles. Due to the inclination, this represents the hypotenuse.
The height is the opposite side. So
[tex]\sin{45} = \frac{h}{13}[/tex]
We have that [tex]\sin{45} = \frac{\sqrt{2}}{2} = 0.71[/tex]
[tex]\sin{45} = \frac{h}{13}[/tex]
[tex]0.71 = \frac{h}{13}[/tex]
[tex]h = 13*0.71 = 9.19[/tex]
The height of the hill is of 9.19 miles.
