Question

A balloon is 300 feet above a cliff. The angle of depression to the cliff edge is 40° 30'. What is the horizontal distance from the balloon to the edge of the cliff?
a. 462 feet
b. 392 feet
c. 351 feet
d. 256 feet

Answer 1

May be the vertical distance is 300.
and let horizontal distance be h.
angle of depression (from the balloon) to edge of cliff = 40.5°
so,
tan(40.5)=h/300
h= 300*tan(40.5)
since, tan(45°)=1, tan(40.5°) must be smaller than one as tan(x) is a increasing function.
so 300*tan(40.5°) must be less than 300
therefore the horizontal distance is 256 ft