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 = [tex]70^\circ[/tex]
A right angled triangle can be constructed for the given situation.
Please refer to the attached figure.
[tex]\triangle BFK[/tex] 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
[tex]\angle B = 70^\circ[/tex]
To find, side FK = ?
We can use sine trigonometric identity to find the value of FK.
We know that :
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\Rightarrow sinB = \dfrac{FK}{BK}\\\Rightarrow sin70 = \dfrac{FK}{65}\\\Rightarrow FK = 65 \times 0.94\\\Rightarrow FK = 61.1\ m[/tex]
Hence, the answer is 61.1 m.
