# Thread: [SOLVED] Angles of Elevation and Depression

1. ## [SOLVED] Angles of Elevation and Depression

the angle of elevation from the top of a small building to the top of a nearby taller building is 46.67 degrees, while the angle of depression to the bottom is 14.17 degrees. If the smaller building is 28 meters high, find the height of the taller building

well i can't really draw the picture and the wording is confusing me, help please

2. Hello, something3k!

The angle of elevation from the top of a small building
to the top of a nearby taller building is 46.67 degrees,
while the angle of depression to the bottom is 14.17 degrees.

If the smaller building is 28 meters high, find the height of the taller building.
Code:
                      * C
*   |
*      |
*         |
* 46.67°     |
A * - - - - - - - * D
|   * 14.17°    |
28 |       *       | 28
|           *   |
B * - - - - - - - * E

The smaller building is: $AB \,=\,DE \,=\,28$
The taller building is $CE.$
$\angle CAD = 46.67^o,\;\angle DAE = 14.17^o$

In right triangle $EDA\!:\;\;\tan14.17^o \:=\:\frac{28}{AD} \quad\Rightarrow\quad AD \:=\:\frac{28}{\tan14.17^o} \:\approx\: 110.9$

In right triangle $CDA\!:\;\;\tan46.67^o \:=\:\frac{CD}{110.9} \quad\Rightarrow\quad CD \:=\:110.9\tan46.67^o \:\approx\:117.56$

Therefore: . $CE \:=\:117.56 + 28 \:=\:145.56\text{ m}$

3. thank you very much i had trouble trying to draw the picture so i messed everything up, thanks again