# Math Help - Frustrating Hmwk DUE

1. ## Frustrating Hmwk DUE

Simi is standing 200 m due east of Raoul. From Raoul, the angle of elevation from the ground to the top of a building due north of Raoul is 12 degrees. From Simi, the angle of elevation from the ground to the top of the building is 9 degrees. Let the height of the building be h m. Express the following in terms of h.
(i) the distance from Raoul to the foot of the building
(ii) the distance from Simi to the foot of the building

I'v been trying to figure this out all day. Could someone please give me a hint on what I should do???

2. 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 $h$ meters.
Express the following in terms of $h$.

(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 $h$ 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: . $\tan12^o \:=\:\frac{h}{x}$
. . Therefore: . $\boxed{x \;=\;\frac{h}{\tan12^o}}$

Simi is looking at a building $h$ 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: . $\tan9^o \:=\:\frac{h}{y}$

Therefore: . $\boxed{y \;=\;\frac{h}{\tan9^o}}$

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

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!

3. lol yes there were two more parts:

b) Use your answers above and Pythagoras' theorem to find the height of the building.

c) On what bearing is the building from Simi?