Question

a plane flying at a certain altitude is observed from two points that are 2.2 meters apart. the angles of elevation made by the two points are 55º and 72º. if the plane is to the east of both observation posts, the altitude of the plane is . nextreset

Answer 1

When you make a drawing with the instructions, and call x the altitude of the plane and y the distance from the angle 72 ° to the point straight below the plane, you obtain these equations

tan(55°) = x / (2.2 + y)

tan (72°) = x / y

You solve y from the second equation

y = x / tan(72°)

Substitute y in the first equation

tan (55°) = x /(2.2 + x/tan(72°)

Solve for x:

x = tan(55)[2.2 + x/tan(72) ]

x = tan(55) (2.2) + x tan(55)/tan(72)

x - x tan (55)/tan(72) = 2.2 tan (55)

Now substitute the values of the tangents

tan (55) = 1.4281
tan(72) = 3.0777

x - 0.464x = 3.1419

x = 3.1419 / (1-0.464) =5.86 m

Ah ... it is a toy plane! I guess.