Question

Isaac and Albert spot a hot air balloon flying at a low altitude. They decide to calculate its height by standing 400 feet apart on a level surface and measuring the angle of elevation to the balloon. From

Albert, the balloon was at an angle of elevation of 62°and from Issac its was 48º. Determine the height of
the balloon above the ground to the nearest foot.

Answer 1

144 feet to nearest foot.

Explanation:

Let the distance between Albert and the point on the ground that the balloon is directly above be x feet Then for Isaac the distance is 400 - x feet

So we have 2 right angled triangles and:

tan 62 = h/x

tan 48 = h / (400- x) where h is the height of the balloon.

From the first equation x = h / tan 62 so plugging this into the second one:

tan 48 = h / ( 400 - h/tan 62)

h = 400 tan 48 - h tan 48 tan 62

h + h tan 48 tan 62 = 400 tan 48

h ( 1 + tan48 tan62) = 400 tan48

h = 400 tan 48 / (1 + tan 48 tan 62)

= 143.8 feet.