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: $\displaystyle AB \,=\,DE \,=\,28$

The taller building is $\displaystyle CE.$

$\displaystyle \angle CAD = 46.67^o,\;\angle DAE = 14.17^o$

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

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

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