Determine the height of the balloon.

Question

While taking a ride in a hot-air balloon in Napa Valley, you wonder how high you are. To find out, you choose a landmark that is to the east of the balloon and measures the angle of depression to be 〖54〗^°. A few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be 〖61〗^°.

Answer 1

You need to draw a triangle where L is the horizontal distance between the landmark and the observer and H is the height of the balloon. Upon reduction of L by 100 feet the angle of depression increases to 61º.

 

H = L tan54º, H = (L-100) tan61º. Hence  100 = H (1/tan54º - 1/tan61º), or H = 100/(cot54º - cot61º). Find the two cotangents and plug in to get your answer for the height.