# Math Help - Trig word problem help

1. ## Trig word problem help

The shadow of a city building is observed to be 100 m long. At the same time the shadow of a lamp post 9 m high is observed to be 5.5 m long. Find the altitude of the sun, and the height of the building.

-----
I'm thinking that since there are no angles given, the proportionality theorem of triangles will be applied. But I have doubts. So, how do you solve this?
Thanks.

2. Originally Posted by fayeorwhatsoever
The shadow of a city building is observed to be 100 m long. At the same time the shadow of a lamp post 9 m high is observed to be 5.5 m long. Find the altitude of the sun, and the height of the building.

-----
I'm thinking that since there are no angles given, the proportionality theorem of triangles will be applied. But I have doubts. So, how do you solve this?
Thanks.
1. Draw a sketch. (see attachment)

2. Use proportions:

$\dfrac h9 = \dfrac{100}{5.5}~\implies~h \approx 163.36\ m$

3. Use the Tangens function to calculate the altitude of the sun (presumeably you mean the angle of elevation above the horizon?)

$\tan(\phi)=\dfrac9{5.5}~\implies~\phi \approx 58.57^\circ$