The straight line piece which is carried out from triangle top in the direction of the opposite party and perpendicular to it is called triangle height. The opposite side is called the basis and as tops and the parties at a triangle on three, and heights on the different bases as much. Depending on the known parameters of a triangle, for calculation of height it is possible to use different formulas some of which are given below.
Instruction
1. Use a formula Ha=2*S/A for finding of height of a triangle if its area (S) and length of the party, opposite are known to a corner from which height (A) is carried out. This the party is called the basis, and height is designated as "height on the basis of A" (Ha). For example, if the area of a triangle is equal to 40 square centimeters, and length of the basis is 10 cm, then height will be calculated so: 2*40/10 = 8 cm.
2. If length of the basis is not known, but length of the party (B), adjacent to it, and a corner between the basis and this party is known (γ), then height (Ha) can be expressed as a half of the work of length of this party on a sine of the known corner: Ha=B*sin(γ). For example, if length of the adjacent party is equal to 10 cm, and the corner makes 40 °, then height can be calculated so: 10*sin (40 °) = 10*0.643 = 6.43 cm.
3. If lengths of all three parties of a triangle are known (A, B and C) and the radius of the circle (r) entered in it, height which is carried out from any of the parties can be expressed as the work of radius of an inscribed circle for the sum of lengths of the parties of a triangle divided into basis length. For example, for height which is carried out from the party of A, this formula can be written down so: Ha=r * (A+B+C)/A.
4. From the previous formula follows that it is not obligatory to know lengths of all parties if length of perimeter (P), length of the basis (A) and radius of an inscribed in a triangle circle (r) are known. Then for calculation of height on the basis of A will be to multiply enough perimeter length on the radius of an inscribed circle and to divide into basis length: Ha=r*P/A.
5. If instead of the radius of an inscribed circle the radius of described (R) and length of all parties of a triangle is known (A, B and C), for finding of height on any basis it is necessary to multiply lengths of all parties, and to divide the received result into the doubled work of radius of a circumscribed circle at basis length. For example, for height which is carried out from the party of A, this formula can be written down so: Ha=A*B*C / (2*R*A).