trig problem...help please

[jferrel8]

The gondola ski lift at a ski resort is 2350 m long. On average, the ski lift rises 13.5 ° above the horizontal. How high is the top of the ski lift relative to the base?

 

[soroban]

Hello, jferrel8!

Did you make a sketch?

The gondola ski lift at a ski resort is 2350 m long.
On average, the ski lift rises 13.5° above the horizontal.
How high is the top of the ski lift relative to the base?

                        * B
                     *  |
          2350    *     |
               *        | h
            *           |
         * 13.5*        |
    A * - - - - - - - - * C

The lift is: .\(\displaystyle AB = 1250\) m.
\(\displaystyle \angle A = 13.5^o\)
The height is: .\(\displaystyle h = BC.\)

\(\displaystyle \text{In right triangle }BCA\!:\;\;\sin 13.5^o \:=\:\frac{h}{2350} \quad\Rightarrow\quad h \:=\:2350\sin13.5^o\)

Got it?