Question

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.

Answers

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°

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