Section 4.6– Number 36
A lighthouse is 2 km from a long straight coastline. Find the rate of change of the
distance of the spot of light from point O with respect to angle θ .
Lighthouse
2 miles
θ
Beam of
Light
x
O
Spot of
Light
Solution:
If we call the distance from O to where the spot of light hits along the shoreline x, we are
then looking for
dx
dt
.
We also have that tan θ =
with respect to time.
dx
dt
= 2 sec2 θ
dθ
dt
x
.
2
Thus x = 2 tan θ . We now take the derivative of each side