Answer
The height of the kite is $32.15m$.
Work Step by Step
From the free-body diagram below, we can see that there are 2 horizontal forces acting in opposite direction:
- The wind force $\vec{F}\cos56$
- The tension force $\vec{T}\cos\theta$
As the kite was hovering at the end of the line, we understand that the kite cannot move further horizontally, so it is static. Therefore, $$T\cos\theta=F\cos56$$ $$\cos\theta=\frac{F\cos56}{T}=\frac{19\cos56}{16}=0.664$$ $$\theta=48.39^o$$
This angle $\theta$ is key to figuring out the height of the kite. On the right side of the image, we can see that the kite makes a right triangle. Therefore, the height $H$ of the kite is $$H=43\times\sin\theta=32.15m$$
