Any solid can be interesting not only to the school student. In the world around, objects in the form of a pyramid quite often meet. And it not only well-known Egyptian tombs. Often speak about curative properties of a pyramid, and someone for certain will want to be influenced by them. But for this purpose it is necessary to know its sizes, including height.
It is required to you
- Mathematical formulas and concepts:
- Determination of height of a pyramid
- Signs of similarity of triangles
- Properties of height of a triangle
- Theorem of sine and cosines
- Tables of sine and cosines
- Tools:
- ruler
- pencil
- protractor
Instruction
1. Remember what is pyramid height. It is the perpendicular lowered from pyramid top to its basis.
2. Construct a pyramid in the set parameters. Designate its basis by Latin letters A, B, C, D... depending on quantity of corners. Top of a pyramid designate S.
3. The parties, corners of the basis and an inclination of edges to the basis are known to you. The drawing will turn out in a projection to the planes therefore for fidelity designate on it data known to you. From a point of S lower height of a pyramid and designate it by h. Height point of intersection with the pyramid basis to S1 oboznchta.
4. From top of a pyramid carry out height of any side side. Designate a point of its crossing with the basis, for example, of A1. Remember properties of height of an acute triangle. It divides a triangle into two similar rectangular triangles. Calculate cosines of corners necessary to you on formulecos (A) = (b2+c2-a2)/(2*b*c) where and, b and with - the parties of a triangle, in this case ASB (a=BA, b=AS, c=AB). Calculate height of a side side of SA1 on a cosine of the angle of ASA1 equal to SBA corner from properties of height of a triangle, and the known side edge of AS.
5. Connect points of A1 and S1. At you the rectangular triangle in which to you the hypotenuse of SA1 and a tilt angle of a side side of a pyramid to its basis is known to SA1S1 turned out. According to the theorem of sine calculate a leg of SS1 which at the same time is also pyramid height.