suggest the diagram?

Question

at the foot of a mountain,the elevation of its summit is 45 degree .after ascending 500m , towards the mountain up an incline of 30 degree , the elevation changes to 60 degree .find the height of the mountain. :)

Answer 1

I notice your question actually asks us to suggest the diagram, not solve the problem for you!
I don't know how to do the diagram on here, but suggest you do this:

Draw a starting point A, then a line from A inclined at 30 deg to the horizontal, ending at point B. Write 500m on this line.
From A draw a line at 45 deg to the horizontal, and from B draw a line inclined at 60 deg to the horizontal. Where they meet is the summit S.

I haven't looked at Helmut's solution, but I expect he's right -- he's pretty good at Maths. Anyway, I think he should have got something like
500 sin 150°/(√2 sin 15°)
On looking, I see it doesn't look much like Helmut's answer, but if you put them both in a calculator I think you'll find they're the same. I like his better than mine. email me if you want to discuss it further.

Now I see you can't email me, because you don't allow email. It's good to allow it: messages go through Yahoo! Answers, and your own address isn't revealed.

Answer 2

h = 500(sin30° + sin60°)
h ≈ 683 m