A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. )
A)45 m
B)41 m
C)43 m
D)49 m
E)47 m

Question

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze,the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place. ) ​
A)45 m
B)41 m
C)43 m
D)49 m
E)47 m

Quizplus · Accepted Answer

To find the height of the balloon, we can use the trigonometric function sine, since we have the angle and the hypotenuse (the length of the tether). The sine of an angle in a right triangle is the opposite side (height of the balloon in this case) over the hypotenuse (the length of the tether). So, sin(55°) = height / 50 meters. Rearranging to solve for height gives us height = 50 * sin(55°). Using a calculator, we find that height ≈ 40.96 meters, which rounds to 41 meters.

A 50-Meter Line Is Used to Tether a Helium-Filled Balloon