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Question

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.

Illustration of situation

Answer 1

construct a right triangle with base = 100, altitude = 50,

the hypotenuse = sqr(100^2 +50^2 = sqr12500 = 111.8 feet from balloon to the observer

or

find the angle A whose tangent = 50/100 = 1/2.

A = tan^-1(1/2) = 26.565

use the law of sines

sin26.565/50 = sin90/h

h = 50/sin26.565 = 111.8 feet

after another 5 seconds the balloon is 100 feet high and a distance of 141.4 feet from the observer

hypotenuse = sqr(100^2 +100^2) = sqr20,000 = 100sqr2 = 100(1.414) = 141.4 feet

or

notice it's a right triangle with two 45 degree angles & use the law of sines

h/sin90 =h/1 = h = 100/sin45 =100/.707 = 141.4 feet