With the informations given by the question, we have the following diagram:
To calculate the height, we have the following trigonometric relation(since it is a right triangle):

Just solving for 'h':
![h=420\cos (60^(\circ))=420*\frac{\sqrt[]{3}}{2}=210\sqrt[]{3}\approx363.7](https://img.qammunity.org/2023/formulas/mathematics/high-school/zg78mcmocz8x98vn828jt0891dic7rzlfb.png)
With this, we have our height. The height of the kite is 363.7 ft