Question

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?

Answer 1

Answer:

Step-by-step explanation:

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

= $800(tan 65-tan 20)\\= 1342.56$

Speed of the boat per second = $\frac{1342.56}{25} \\=53.702$

53.702 feet per second is the speed of boat