from a point on the ground the angle of elevation of the bottom and top of a flagstaff situated on top of a 120 m tall house is 30 and 45 degrees respectively.find the height of the flagstaff.

Answer 1

you know that the point on the ground is
240m from the bottom of the pole
120√3 m from the base of the house

so, in the 45° triangle,

120+h = 120√3
h = 120(√3-1) = 87.846 m

or using the law of cosines,

h^2 = 240^2 + 120^2*3+(120+h)^2 - 2(240)*√(120^2*3+(120+h)^2)*cos15°