Hello, topaz192!

You have the right idea, but you need a better diagram.

An incline that transports passengers up and down a mountain,

has an angle elevation of 30°. From a point horizontal 100 ft from the base,

the angle of elevation to the top is 26.8°.

What is the lengh of the track? Code:

* B
* * |
* * |
* * |
* * |
* * |
* * |
* 26.8° 150° * 30° |
* - - - - - - - * - - - - - - - *
D 100 A C

We have: .$\displaystyle \angle BAC = 30^o \quad\Rightarrow\quad \angle BAD = 150^o$

. . and: .$\displaystyle DA = 100,\;\angle D = 26.8^o$

In $\displaystyle \Delta BAD,\;\angle DBA \;=\;180^o - 26.8^o - 150^o \;=\;3.2^o$

Law of Sines: .$\displaystyle \frac{AB}{\sin26.8^o} \:=\:\frac{100}{\sin3.2^o}$

Therefore: .$\displaystyle AB \;=\;\frac{100\sin26.8^o}{\sin3.2^o} \;=\;807.7129786$ feet.