Question

two observer p and r 15 meters apart observes a plane in the same vertical plane and from the same side of the kite,the angles of elevatio of the plane from p and r are 30 60 respectively.find the height of the plane to the nearest meter.

Answer 1

Let the plane's position be labelled A, and the bottom of the vertical B
In triangle APR, angle A = 30° using basic geometry.
Then PR = AR = 15, since we now have an isosceles triangle.
then sin60° = AB/AR
AB = 15sin60 = appr 12.99 or 13 metres

Answer 2

if the height of the plane is h, then
h cot30° - h cot60° = 15

Answer 3

Hor. distance of P = X meters.
Hor distance of R = x-15 meters.

Tan30 = h/x
h = x*Tan30.

Tan60 = h/(x-15)
h = (x-15)*Tan60.

h = x*Tan30 = (x-15)Tan60
0.58x = 1.73x-26
X = 23 m.

h = x*Tan30 = 23*0.58 = 13 m.