The height above the ground the kite is flying is 62.28 meters
<em><u>Solution:</u></em>
Given that Brains kite is flying above a field at the end of 65 m of string
The figure is attached below
ABC is a right angled triangle
Let AB be the height at which the kite is flying above the ground
AB = h = ?
Given that angle elevation to the kite measures 70 degrees
Thus angle C = 70 degrees
Brains kite is flying above a field at the end of 65 m of string
Therefore, AB = 65 meters
We know that,
![sin \theta = \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=sin%20%5Ctheta%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
Here,
![\theta = 70^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2070%5E%7B%5Ccirc%7D)
Opposite = AB = h
Hypotenuse = AC = 65 meters
Therefore,
![sin 70 = \frac{h}{65}\\\\0.9397 = \frac{h}{65}\\\\h = 0.9397 \times 65\\\\h = 61.08](https://tex.z-dn.net/?f=sin%2070%20%3D%20%5Cfrac%7Bh%7D%7B65%7D%5C%5C%5C%5C0.9397%20%3D%20%5Cfrac%7Bh%7D%7B65%7D%5C%5C%5C%5Ch%20%3D%200.9397%20%5Ctimes%2065%5C%5C%5C%5Ch%20%3D%2061.08)
To find the height above the ground we have to add 1.2 m to 61.08
height above the ground = 61.08 + 1.2 = 62.28 meters
Thus the height above the ground the kite is flying is 62.28 meters