Question

Johnny title balloon to a rock and placed it in his backyard. The balloon string is 13 feet long and the wind blows the balloons so that makes up 45° angle from the ground if the balloon is now 12 feet away from the rock how far off the ground is The ballon?

Answer 1

Using trigonometry, the height of the balloon from the ground is found by multiplying the sine of the 45° angle by the 13-foot length of the string. The calculations reveal the balloon is approximately 9.2 feet off the ground.

Step-by-step explanation:

To solve for the height of the balloon off the ground, we can use trigonometry as the question describes a right triangle, where the balloon string represents the hypotenuse, the distance from the rock to the point on the ground right below the balloon is the adjacent side, and the height of the balloon off the ground is the opposite side. Given that the angle from the ground is 45° and the string's length is 13 feet, which is the hypotenuse, we can use the sine function to find the height:

Sine(45°) = Opposite / Hypotenuse
Sine(45°) = Height / 13 feet
Height = 13 feet * Sine(45°)
Since the sine of 45 degrees is √2/2, the height of the balloon will be:
Height = 13 feet * (√2/2) = 13/√2 feet
Height = approximately 9.2 feet

Therefore, the balloon is approximately 9.2 feet off the ground.