# pre cal

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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?

• pre cal -

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

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