A balloon is hovering 800 ft above a lake. The balloon is observed by the crew of a boat as they look upwards at an angle of 20 degrees. Twenty-five seconds later, the crew has to look at an angle of 65 degrees to see the balloon. How fast was the boat traveling in feet per second?

given that a balloon is hovering 800 ft above a lake. The balloon is observed by the crew of a boat as they look upwards at an angle of 20 degrees. Twenty-five seconds later, the crew has to look at an angle of 65 degrees to see the balloon

The distance of the boat from the balloon measured horizontally in the I position = 800 tan 20

After 25 seconds distance of the boat from the balloon measured horizontally in the II position

= 800 tan 65

Distance moved by the boat in 25 seconds

= [tex]800(tan 65-tan 20)\\= 1342.56[/tex]

Speed of the boat per second = [tex]\frac{1342.56}{25} \\=53.702[/tex]

53.702 feet per second is the speed of boat