Answer:
61.1 m is the correct answer.
Step-by-step explanation:
Given that
Brittany's kite has a string length = 65 m
Angle of elevation of kite = ![70^\circ](https://tex.z-dn.net/?f=70%5E%5Ccirc)
A right angled triangle can be constructed for the given situation.
Please refer to the attached figure.
in which B is the position of Brittany.
K is the position of kite and
F is the point of field above which the kite is flying.
Given that the side BK = 65m
![\angle B = 70^\circ](https://tex.z-dn.net/?f=%5Cangle%20B%20%3D%2070%5E%5Ccirc)
To find, side FK = ?
We can use sine trigonometric identity to find the value of FK.
We know that :
![sin\theta =\dfrac{Perpendicular}{Hypotenuse}](https://tex.z-dn.net/?f=sin%5Ctheta%20%3D%5Cdfrac%7BPerpendicular%7D%7BHypotenuse%7D)
![\Rightarrow sinB = \dfrac{FK}{BK}\\\Rightarrow sin70 = \dfrac{FK}{65}\\\Rightarrow FK = 65 \times 0.94\\\Rightarrow FK = 61.1\ m](https://tex.z-dn.net/?f=%5CRightarrow%20sinB%20%3D%20%5Cdfrac%7BFK%7D%7BBK%7D%5C%5C%5CRightarrow%20sin70%20%3D%20%5Cdfrac%7BFK%7D%7B65%7D%5C%5C%5CRightarrow%20FK%20%3D%2065%20%5Ctimes%200.94%5C%5C%5CRightarrow%20FK%20%3D%2061.1%5C%20m)
Hence, the answer is <em>61.1 m.</em>