Height of chimney stack using Angles of Elevation

• Apr 29th 2011, 11:42 AM
dmi3
Height of chimney stack using Angles of Elevation
Hello, can anyone help me out with this:

At a point А due south of a chimney staсk, the angle of elevation
of the staсk is 55 degrees. From B, due west of А, such that АB = 100
m, the elevation of the staсk is 33 degrees. Find the height of the stake
and its horizontal distance from А.
• Apr 29th 2011, 12:52 PM
TheEmptySet
You have to draw a diagram to see what is happening.

Attachment 21495

Sorry I still can't upload images but here is a PDF with the pictures.

From this we can use the Pythagorean theorem to get

$\displaystyle d_1^2+100^2=d_2^2$

Now using the angles of elevation we get

$\displaystyle \tan(55^{\circ})=\frac{h}{d_1} \iff d_1=\frac{h}{\tan(55^\circ)}$

$\displaystyle \tan(33^{\circ})=\frac{h}{d_2} \iff d_2=\frac{h}{\tan(33^\circ)}$

Now just plug $\displaystyle d_1,d_2$ into the first equation and solve for h.
• Apr 30th 2011, 12:10 AM
dmi3
Oh now i get it... Thanks a lot!