For this problem, we are given a triangle and we need to determine its height.
The distance of the UFO from point A is equal to the side c of the triangle, this side forms a right triangle with the height, where the height is the opposite cathetus from angle alpha and side c is the hypothenuse. We can use the sine relationship to determine the height, as shown below:
[tex]\begin{gathered} \sin(87.4)=\frac{h}{425.58}\\ \\ h=425.58\cdot\sin(87.4)\\ \\ h=425.58\cdot0.9989706=425.14 \end{gathered}[/tex]
The height is approximately 425.14 km.
