Having trouble understanding word probl Trig.

[Miike012]

Homework Statement

rock rises straight upward frim the valley floor. From one point the angle of elevation of the top of the rock is 16.7 deg. From a point 168 m closer to the rock the angle of elevation of the top of the rock is 24.1 deg. How high is the rock...

I added an attachment... What I thought was correct I did in red... but the way my solution guide had it is in black... I don't understand how their way works.. can some one please help me understand... thank you...

If I understand this, this will help me understand all the other word problems that are similar... I would appreciate it.. thank you.

Homework Equations

The Attempt at a Solution

 

[eumyang]

Oh yes, the part in red is completely wrong. Imagine you are standing at the vertex of the 16.7° angle of elevation (which I will call point A). When it says "from a point 168 m closer to the rock," you walk to the right (according to your diagram), 168 m closer to the base of the rock (which I will call point C). Now you are at the vertex of the 24.1° angle of elevation (which I will call point B). That is why the distance between A and B (the two vertices) is 168 (in black) and not x (in red). For some reason you're thinking that the distance BC is 168 m less than the distance AB, and that is not correct. The distance BC is 168 m less than the distance AC. And since we don't know the distance BC, we call it x (in black).

 

[Miike012]

Thank you.. I understand now... thanks a lot!