pre cal
posted by karina on .
Tamara is flying in a hot air balloon. The hot air balloons is flying at an altitude of 1100 feet. The ground distance to the landing site is 1400 feet.
What is Tamara's angle of depression to the landing site?
What is the actual distance between the hot air balloon and the landing site?

If you sketch this out you will have a right triangle, I will call ABC.
A is the vertex = angle of depression
AC (side b) = base = 1400 feet
BC (side a) = leg = 1100 feet
AB (side c) = hypotenuse = distance to landing site
To find angle A (angle of depression)
tan A = a/b = 1100/1400 = 0.7857
tan A = 0.7857
arctan 0.7857 = 38.16 deg
To find C (distance to airport)
c^2 = a^2 + b^2
c^2 = 1100^2 + 1400^2
c^2 = 1,210,000 + 1,960,000
c^2 = 3,170,000
c = 1780.45 feet
1780.45/5280 feet in mile = 0.34 miles