Sarah holds the end of her kite string 5 feet off the ground. The kite string makes a 43 degree angle of elevation with the horizontal and the kite is 105 ft. off the ground. How long is the kite string to the nearest tenth of a foot?
cos43=100/x ?
(105-5)/x = sin43°
To find the length of the kite string, we can use the trigonometric relationship involving the cosine function.
Let's define a right triangle with the ground as the horizontal side, the kite string as the hypotenuse, and the vertical side connecting the ground to the kite.
We know that:
- The height of the kite from the ground is 105 feet.
- The height of the string from the ground is 5 feet.
- The angle of elevation between the ground and the string is 43 degrees.
Now, let's apply the cosine function:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is the height of the kite from the ground (105 ft), and the hypotenuse is the length of the string.
cos(43 degrees) = 5/x
Where x represents the length of the kite string.
To solve for x, we can rearrange the equation:
x = 5 / cos(43 degrees)
Now, we can calculate the length of the kite string:
x ≈ 7.22 feet
Therefore, the length of the kite string, to the nearest tenth of a foot, is approximately 7.2 feet.