Question

a hill is inclined at 18 degrees to the horizontal. If the base of the hill is at sea level find
a. my height above sea level if I walk 1.2 km up the hill
b. how far I have walked up the hill if I am 500 metres above sea level.

Answer 1

Using simple right triangle trig, the sine is define as the ratio of the side opposite the known angle to the hypotenuse of the triangle, thus
sin18=x/1.2
or
x=1.2sin18=.37 km approximately
(see drawing to follow)

Answer 2

For part (b) you can use the sine again since the given info involves the opposite side and the hypotenuse:
sin18=500/y
or
y=500/sin18=1618 km approx.
(again see drawing)