Trig Functions?

[MelleWinn]

"A rocket rises vertically. A and B are both standing due north of the launch pad and are 1 km apart. At a certain moment, the angle of elevation of the rocket for A is 30 degrees, and the angle of elevation for B is 40 degrees. How high is the rocket?

 

[HallsofIvy]

Yes that requires the use of trig functions! If you draw a picture, you should see that you have two right triangles. Let "x" be the distance from B to the launching part, "h" the height of the rocket, both in km. Then h/x= tan(40). A is 1 km farther away- x+1 and h is still the same. h/(x+1)= tan(30).
The easy part is to divide equation by the other to get rid of h: (h/x)(x+1/h)= x/(x+1)= tan(40)/tan(30). Solve that for x. Once you know x, h= xtan(40).

 

[JeffM]

In fact, it was to answer questions of this kind that trigonometry was first invented.