A highway has a gradient of 0.087. How many meters would an automobile rise vertically if it traveled 2 miles along the way?

$\tan \theta = 0.087$

$\theta = 4^\circ 58' 19.97"$
 

 

$\sin \theta = \dfrac{\text{rise}}{2}$

$\text{rise} = 2 \sin \theta$

$\text{rise} = 2 \sin (4^\circ 58' 19.97")$

$\text{rise} = 0.1733 ~ \text{mile}$

$\text{rise} = 0.1733 ~ \text{mi} \times \dfrac{5280 ~ \text{ft}}{1 ~ \text{mi}} \times \dfrac{1 ~ \text{m}}{3.28 ~ \text{ft}}$

$\text{rise} = 279.04 ~ \text{m}$