Hello, xwrathbringerx!

I assume there are *more* parts to this problem.

(Otherwise, there is way too much information!)

As written, it can be separated into two simple problems.

Simi is standing 200 m due east of Raoul.

From Raoul, the angle of elevation to the top of a building due north of him is 12°.

From Simi, the angle of elevation to the top of the building is 9°.

Let the height of the building be meters.

Express the following in terms of .

(i) the distance from Raoul to the foot of the building

(ii) the distance from Simi to the foot of the building

Raoul is looking at a building meters high.

His angle of elevation to the top of the building is 12°.

How far is Raoul from the foot of the building? Code:

*
* |
* |
* | h
* |
* 12° |
R * - - - - - - - - *
x

In this right triangle: .

. . Therefore: .

Simi is looking at a building meters high.

His angle of elevation to the top of the building is 9°.

How far is Simi from the foot of the building? Code:

*
* |
* |
* |
* |
* 9° |
* - - - - - - - - *
y

In this right triangle: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

If that is *all* the question wanted, we didn't need to know that:

. . Simi is 200 meters east of Raoul,

. . the building is north of Raoul.

In fact, they don't have to be looking at the same building.

. . Raoul and Simi could be on two different planets!