Question

From a balloon 915 feet high, the angle of depression to the ranger headquarters is 85°14'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Answer 1

so to convert \(\bf 85^o14'\) to decimals, just divide the 14/60 = 0.23
so \(\bf 85^o14' = 85.23^o\)

Answer 2

the the tiny smaller "complementary" angle will be 90- 85.23 = 4.77
know keep in mind that you have

so you have the "adjacent" side of that right-triangle, and the angle, and you want "b" side

which trig identity uses the adjacent side and the angle and the "opposite" side?
http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png

Answer 3

tan = opp/adj