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if you are something of a masochist then you could do it the old fashioned way-stand at mean high water ( which i believe is on newlyn pier, but i could be wrong) with a theodolite, then take measurements of the furthest point in line of sight in the direction of the place you wish.( having a freind with one of those stripey poles helps).Measure the straight line distance to the point. then stand at that point and measure another point, again in line of site in the right direction. carry on doing this till you get to the point you want. simple trig allows you to calculate the height( height of point = straight line distance*sine of the angle subtended.). If this sounds laborious, it is. but the himalayas were mapped in this way to an accuracy measured in feet.
In what way it his answer tripe? That is exactly the way that heights had to be measured before accurate altimeters were invented...though I would dispute the accuracy level given as when K2 was measured by GPS it was discovered to be over 50 metres taller than first thought and until everest was remeasured was the highest mountain for a few days.
Being an ex civil engineer, I can vouch that incitatus' answer, whilst a little simplified, is more ot less correct. I know; I have done it. Did you know that when Everest was first measured the height was calculated at 29000 feet exactly. It was thought this sounded like a guess, so the official height was 29002 feet.
Maude, rather depends on why alextwo has posed the question. The 'spirt level' technique is the most accurate way of measuring height and this technique will have been used to measure the height/depth of most common land features - if you are interested in how maps where constructed this is the method that would be interested in. Contour lines, altitude or GPS are also valid (they either depend on the spirit levels techniques mentioned above or are much less accurate) . You would of course use these techniques if you are trying to determine you own current height above sea-level e.g. you are a hill-walker or climber. As Alextwo has not responded, I suppose we shall never know.
maude dearset, dont throw accusations of cowstomachlining around unless you know whereof you speak. this was the standard method until a few years ago. indeed reconning from trig points can still be more accurate than gps as the american military code gps to diminish its accuracy for non military purposes. Many altimeters work either by gps, reckoning height from ground and reconciling with a map (useless here) dead inertial reckoning (similarly dodgy) or pressure variation (very suspect)
I stand far enough back from you to see the top of your pointy head. planting the theodolite(or protractor) on the ground i take a view through the telescope to the top of your head. i resist the temptation to shoot. I note the angle to the top of your head. Given tht this is 1856 and laser rangefinders have not been invented I adjust my position until the angle is 45 degrees. the distance to the centre of the column is now equal to the distance to the top of your head from the top of the theodolite. If you add on the height of the theodolite you get your height. This should be accurate to inches. If there is no room to get a 45 degree angle, or it is impractical, the distance to the top of the hill along the line of sight can be used. The vertical distance is equal to the sine of the subtended angle multiplied by the straight line distance. I could ask you to hold a peice of string which we could later measure ( this is done for short distances such as on building sites) or i could do this by taking bearings from two different buildings/p[oints a known distance apart and calculating the distance using euclidean geometry. Really i fail to see what is difficult about the concept. we surveyed the trees in our school playground like this when I was 9 and it is very basic maths.