Triangle Math Problem

Question

A photographer set up a camera 100 feet away from a launching spot of a hot air balloon. When the photographer takes her first picture, she elevates the camera 75 degrees to center the balloon in the picture. When she takes a second picture a minute later, she elevates the camera 80 degrees to center the balloon in the picture. Assuming the balloon remains above the launching pad at all times, how many feet has it risen in the minnute?

Answer 1

"a"=100

"β"=75°

"γ"=90°

so "α"=15°

"β2"=5°+75=80°

"b2"=?

"α2"=10°

a/sinα=b/sinβ=c(right angle)

100'/sin15=386.37=b/sin75 ; b=373.205'

100/sin10=575.877=b2/sin80; b2=567.128

-=193.923' (difference)

Answer 2

Draw a right triangle and note

tan(θ) = y / x

where

θ = angle of elevation

y = balloon height above launch pad

x = horizontal distance to launch pad (100ft)

Solving for y:

y = x⋅tan(θ)

So the change in height is:

100⋅tan(80) - 100⋅tan(75) = 100 ⋅ [ tan(80) - tan(75) ]

You can complete the calculation, be sure to use degree mode ('deg') on your calculator or convert the angles to radians ('rad').

193.9 ft