We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

The angle of elevation of the top A of a building from a point C due south of it is 25 degrees. At a second point D, which is 160 metres due west of C, the angle of elevation of the top of the building is 20 degrees. Point B is the bottom of the vertical building and on the same horizontal plane as D and C.

- Find the height of AB of the building to the nearest metre.

Guest Jun 19, 2014

#1**+14 **

Best Answer

Let C be the point (0,0,0)

Then D is (-160,0,0)

B is (0,y,0)

A is (0,y,z)

From what we are given

$$\tan(25deg) = \dfrac z y$$

$$\tan(20deg) = \dfrac{z}{\sqrt{160^2+y^2}}$$

solving this we get

z=93.16m which is the the length of AB, i.e. the height of the building

Rom Jun 19, 2014

#2**+5 **

Using the information in the first part of the problem, let d be the distance from C to B and h be the height of the building. So we have,

tan(25) = h/d Solving for h we have, h = d*tan(25)

And, since we have a right triangle with two legs d and 160, the distnce that D is from B = √(160^{2} + d^{2})

So we have

tan(20) = (h)/√(160^{2} + d^{2}) = (d*tan(25)) / √(160^{2} + d^{2})

Simpifying, we have

tan(20)/ tan(25) = d/√(160^{2} + d^{2}) and we can write

tan(25)/tan(20) = √(160^{2} + d^{2}) /d Square both sides

[tan(25)/tan(20)]^{2} = (160^{2} + d^{2})/d^{2} and the right side = 160/d^{2} + 1 Subtract 1 from both sides

([tan(25)/tan(20)]^{2} - 1) = 160^{2}/d^{2} and we can write

d^{2} = 160^{2} / ([tan(25)/tan(20)]^{2} - 1) Simplifying this, we have

d^{2} = 160^{2} / (.6413959572703699169) Now....take the square root of both sides

d = 199.7822378461935026188794268 m

And using .... h = d*tan(25) ....we have....

h = (199.7822378461935026188794268)* tan(25) ≈ 93.159 m or just 93 m

I think that's it.....I haven't worked one like this before....thanks for submitting it....I hope I haven't made any grevious mistakes !! (P.S. ....thanks to * alan *for catching my previous error.....I went back and corrected it so that now, it appears that I'm smarter than I might really be....also..

CPhill Jun 19, 2014