Question

There is a plot in the shape of an equilateral triangle. A flagstaff is erected at its centroid .Three ropes are tied to the top of the flagstaff and the other ends are nailed at the three corners of the plot. The angle of elevation of the top of the flagstaff at any vertex is 60 degree .What will be the height of the flagstaff (in metres),if the plot is 15m?​

Answer 1

Answer:

Height of flagstaff= 18.37 m

Step-by-step explanation:

Let ABC is an equilateral triangle in which AB=BC=CA=x m (let).

Medians AD , BE and CF of ∆ABC meet at point O, on which a flagstaff VO = 15 m high is

stands there such that angle AVB=angle BVC = angle CVA= 60°(given)

Thus , ∆AVB,∆BVC and ∆ CVA are also equilateral triangles of side length x m.

In right angled triangle ODB

BD/OB=cos30° => BD=OB.cos30°

or. x/2= OB.√3/2. => OB = x/√3……….(1)

In right angled triangle VOB

VB^2= VO^2+ OB^2

(x)^2 = (15)^2+(x/√3)^2

x^2- (x^2)/3 = 225

2.x^2=675

or, x^2. = 337.5

or, x. = 18.37 m