a kite is flying at an angle of elevation of about 40 degrees. all 80 meters of string have been let out. ignoring the sag in the string, find the height of the kite to the nearest 10 meter
h/80 = sin 40°
To find the height of the kite, we can use trigonometry. Let's break down the information we have:
1. The kite is flying at an angle of elevation of 40 degrees.
2. The length of the string is 80 meters.
Now, we can visualize the situation and set up a right triangle:
```
/
/|
/ |
/ |
/ | h (height of the kite)
/ |
/θ |
/______|
x (distance from the person to the kite)
```
In this triangle, the angle of elevation (θ) is 40 degrees, the side opposite the angle of elevation is the height of the kite (h), and the side adjacent to the angle of elevation is the distance from the person to the kite (x).
We know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. Therefore, we can use the tangent function to solve for x:
tan(θ) = h / x
Now, we can rearrange the equation to solve for h:
h = x * tan(θ)
Since we are given the length of the string (80 meters), we can find x by subtracting the height of the person from the length of the string:
x = 80 - height of the person (let's assume an average height of 1.7 meters)
x = 80 - 1.7 = 78.3 meters
Now, we can substitute the values into the equation to find the height of the kite:
h = 78.3 * tan(40°)
Using a scientific calculator, calculate the value of tan(40°) and multiply it by 78.3 to get the height of the kite.
The height of the kite, to the nearest 10 meters, is the final result.