A road goes down a slope. For every 12 km measured along the ground, the road drops 500 m in elevation. a) What is the angle of slope on the road?

b) What is the map distance along the road for every 12 km actually traveled? (measured in km)

c) What is the map distance along the road for every 1 mile actually traveled? (measured in miles)

a) 2.24°

b) 11.99 km

c) 0.9992 miles

Explanation:

We can think of the road as a triangle with a 12 km hypotenuse and a 0.5 km side. Then:

l = 12

h = 0.5

and

sin (a) = h / l

a = arcsin (h / l)

a = arcsin (0.5 / 12)

a = 2.24°

That is the slope.

The map distance travelled would be the other side of the triange.

cos (a) = d / l

d = l * cos (a)

d = 12 * cos (2.24) = 11.99 km

And for miles

d = 1 mile * cos (2.24) = 0.9992 miles