Triangle Problem

Hey guys my uncle is a landscaper and he has a problem for me to solve.

He has a house on a hill. The hills bottom is at the left and it ascends to the right. He has the height of that and at the top of the hill it stops ascending.
Well now you have to imagine that hill as a triangle


The only bit of the triangle he knows is the hills lengtht which he has measured. He wants to know the height of the hill. So with only one measurement of the triangle I have to figure out something before I can use my triginomatiry calculator.
I thought that the easiest angle to figure out would be the one at the top.
The top right angle. Remembering that this is real life not a triangle that you can use a ruler or triangle. I then took the approach of making it into a rectangle.




So if I could figure out the angle with the top right of the angle joining on the triangle then I could figure out the angle in the triangle and figure out the height

Any ideas how to get a pricise measurement using the rectangle or any other way?

If you really need to know the height there are probably much better ways of finding it. If this is just some problem you want solved in this way though, then measuring the angle is probably worth a try.

If you stand at the point down the hill where the length of the hill was measured, and 'aim' some binoculars or something at the house, you can then simply measure the angle the binoculars make with the ground and you have your angle.
This won't be extremely accurate though since the ground is probably not perfectly level.

Far easier would be to get a detailed map of the area and simply measure the distance from the point the length of the hill is measured to the house (but this time not over the ground, but 'in the air' so to speak, parallel to flat ground). You now have two sides of a triangle and you can calculate the third.

The easiest probably is to buy a map showing heights... Or use an accurate altitude meter...

I like the detailed map suggestion

If you don't need much accuracy, you can stack several meter sticks at the bottom of the hill and eyeball the height. You can make it more accurate by using a level on the meter sticks to make sure they're vertical, and by using another level (this time parallel to the ground) to 'aim' at the right place on the meter sticks from the top of the hill. I mostly suggest this because you probably already have the meter sticks and levels, while you might need more work to get a good topographic map of the area.

Make a "horizontal accelerometer" with a protracter, string and a nut or something. http://www.exo.net/~pauld/books/car_...lerometer.jpegMeasure the angle of the top of the hill, then move strait forward from that point toward(or away) from the hill and measure the 2nd angle.(BE SURE TO MEASURE THE DISTANCE BETWEEN POSITION 1 AND POSITION2) This is the "d". Now use this formula: h=(sin(angle1)*sin(angle2))/(sin(angle2-angle1)) * d + your height. MAKE SURE THAT ALL THE UNITS YOU USE ARE THE SAME. IF YOU MEASURE THE D IN FEET THEN USE YOUR HEIGHT IN FEET(5.39FT) NOT IN INCHES. That should give you the height.