Word problem

[jeckelm]

I am confused on how to label the triangle for this word problem.

A straight trail with a uniform inclination of 15 degree's leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 6500 feet. What is the length of the trail?

Also, I need help on tan-1 (tan 5pie/7))

thanks

 

[soroban]

Hello, jeckelm!

A straight trail with a uniform inclination of 15 degree's leads from a lodge at an elevation of 800 feet
to a mountain lake at an elevation of 6500 feet.
What is the length of the trail?

                              *
                          *   |
                L     *       |
                  *           | 5700
              *               |
          * 15deg             |
      * - - - - - - - - - - - *
      |                       |
  800 |                       | 800
      |                       |
      * - - - - - - - - - - - *

\(\displaystyle \text{In the right triangle: }\:\sin 15^o \:=\:\frac{5700}{L}\)

\(\displaystyle \text{Therefore: }\:L \;=\;\frac{5700}{\sin15^o} \;\approx\;22,\!023.1\text{ ft}\)

 

[fasteddie65]

Also, I need help on tan-1 (tan 5?/7))

5?/7 is in Quadrant II.
5?/7 - ? = -2?/7

So tan-1 (tan 5?/7) = tan-1 (tan (-2?/7)) = -2?/7

You have tor remember that the range of the tan-1 function is -?/2 to ?/2.