A flagpole is mounted on top of a tall building. At a distance of $250$m from the base of the building, the angles of elevation of the bottom and the top of the flagpole are $38^\circ$ and $40^\circ$ respectively. Calculate the height of the flagpole, correct to one decimal place. Ok so I know the answer is $14.5$m, but I don't know how to solve it or do the working out? Why does the angle of elevation have $2$ angles, can someone please explain this problem? Thank you.
[Math] Elevation and depression, trigonometry.
trigonometry
Related Solutions
BF is the ground level.
Write EG in terms of angle $50^\circ$.Find $x$. Then the height will be $x\tan 46^\circ + 10$
As pointed out, draw a diagram.
Let the height of the second observation point (above the ground) be h m.
Then, that of the first observation point is h + 2*12 m.
Assume that the flagpole is x m away from the tower.
You now have two right angled triangles with sufficient data to let you setup 2 equations to eliminate x and get h.
Don't forget the required height is h + 2*12 m.
Best Answer
Define $\,b=$ height of building, $\,f=$height of flag, then basic trigonometry gives
$$\tan 38^\circ=\frac b{250}\implies b=250\tan38^\circ\\{}\\ \tan40^\circ=\frac{f+b}{250}\implies f+b=250\tan40^\circ$$
and thus we get that
$$f=250(\tan40^\circ-\tan38^\circ)=14.453$$