A kite is 32m above from the ground. The angle the kite string makes
with the ground is 39°. How long is the kite string, to the nearest metre?
L = h/sinA = 32/sin39 = 51 m.
To find the length of the kite string, we can use trigonometry.
Let's assume the length of the kite string is "x" meters.
We have a right triangle formed with the ground, the kite string, and the height of the kite.
The angle between the ground and the kite string is given as 39°.
Using the trigonometric function "cosine," we can relate the length of the kite string, the height of the kite, and the angle:
cos(angle) = adjacent/hypotenuse
cos(39°) = 32/x
To find x, we can rearrange the equation:
x = 32 / cos(39°)
Calculating the value:
x ≈ 32 / cos(39°) ≈ 40.62
Therefore, the length of the kite string is approximately 40.62 meters, to the nearest meter.
To find the length of the kite string, we can use trigonometry. We have the height of the kite above the ground and the angle the string makes with the ground. We can use the tangent function to find the length of the string.
1. The tangent function is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to it. In this case, the length of the side opposite the angle is the height of the kite, and the length of the side adjacent to it is the length of the string.
2. Let's denote the length of the string as "x". We can set up the following equation:
tangent(39°) = height of the kite / length of the string
tan(39°) = 32m / x
3. Now, we can solve for "x" by multiplying both sides of the equation by "x" and dividing both sides by tan(39°):
x = (32m / tan(39°))
4. Finally, we can substitute the value of tan(39°) into the equation and calculate the value of "x":
x = (32m / 0.809)
x ≈ 39.53m
Therefore, the length of the kite string, to the nearest meter, is approximately 40 meters.