a balloon is tethered to the ground by a string 5 m long if the string makes an angle of 65 degrees with the ground how high above the ground is the balloon
In this problem use Sin functions to solve.
Sin(90) / 5
and set that equal to...
Sin(65) / x
and see what you come up with
The height should be somewhere around 4.5
h = 5*sin65 = 4.53 m.
To find the height of the balloon above the ground, we can use trigonometry and the given information.
First, let's draw a diagram to visualize the scenario:
/|
/ |
/ |
/ |
/ |
/ | 5 m (string)
/______|
------
65°
In the diagram, the string is represented by the line segment that forms an angle of 65 degrees with the ground. We want to find the height of the balloon, which is represented by the vertical line segment.
Now, we can use the sine function to determine the height of the balloon.
sin(angle) = opposite / hypotenuse
In this case, the opposite side is the height of the balloon, and the hypotenuse is the length of the string (5 m).
sin(65°) = height / 5
To find the height, we rearrange the equation:
height = sin(65°) * 5
Using a scientific calculator, we can find the sine of 65 degrees:
sin(65°) ≈ 0.9063
Now we can substitute this value back into the equation:
height ≈ 0.9063 * 5
height ≈ 4.5315 m
Therefore, the balloon is approximately 4.53 meters above the ground.