# Math Help - Height of chimney stack using Angles of Elevation

1. ## 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.

2. You have to draw a diagram to see what is happening.

Stack.pdf

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

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

Now using the angles of elevation we get

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

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

Now just plug $d_1,d_2$ into the first equation and solve for h.

3. Oh now i get it... Thanks a lot!