use Pythagoras' theorem
A balloon rises at a rate of 10 feet per
second from a point on the ground 100 feet from an observer.
a) Find the distance from the observer to
the balloon when the balloon is 50
feet off the ground.
b) After another 5 seconds have passed,
find the distance from the observer to
the balloon. Re-draw the figure to
illustrate this new situation.
a) Draw a right triangle, with the height being the distance above the ground and the base being the distance along the ground from the observer. Use the Pythagorean Theorem to find the hypotenuse, being the line-of-sight distance from the observer.
b) How many feet does the balloon rise in one second? So how far has it risen in five seconds? So what is the new height?
Draw a new right triangle with this new height, and follow the same procedure to find the new distance.