Answer: 0.229 mile = 1210.3 feet
Step-by-step explanation:
Draw a 90° triangle and label the following (see attachment):
- base angle = 10°
- length of the base = 1.3 mile
- height = x
Since the information given is adjacent to the angle and the information needed is opposite of the angle, we can use tan to solve for the height.
[tex]tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 10^o=\dfrac{x}{1.3}\\\\\\1.3\cdot tan\ 10^o=x\\\\.\qquad 0.229=x[/tex]
Since we don't usually measure height of a building in miles, let's convert it to feet (1 mile = 5280 feet)
[tex]0.229\ miles \times\ \dfrac{5280\ feet}{1\ mile} =1210.3\ feet[/tex]
