A surveyor at seal level observed that the of elevation of the of a mountain from point N and P due west of it are 16 degree and 18 degree respectively as shown in the diagram if LNPL is 1600m and the base of the mountain is vertically below m, calculate the height of the mountain.
Trying to interpret what you are saying .....
"LNPL is 1600m.." , no idea where L is, will assume NP = 1600 m
"the base of the mountain is vertically below m" .... HUH?
will assume you want the height of the mountain, I will label it h (for height)
I will label the top of the mountain as R
Look at triangle NPR
you have angle N = 16°, angle NPR = 162° , leaving angle NRP = 2°
also NP = 1600
by the sine law: PR/sin16 = 1600/sin2
PR = 12,636.85 m
now PR becomes the hypotenuse of the triangle that you should see
in your diagram, we can use
sin18 = h/12,636.85
h = 12,636.85sin18 = 3,905 m
For this particular setup, there is an actual formula
I would use:
height = 1600/(cot16 - cot18)
= 3905 m
look at your diagram and see how this fits, or better yet, see if you
can develop that formula
you have mangled the description, but I am assuming that N and P are 1600m apart. You don't say where L is. In any case, if you review your basic trig functions, the height h is seen to obey
h cot16° - h cot18° = 1600
now just find h