Instruction

1

The length of the base (b) isosceles triangle in which the length of the lateral side (a) and the magnitude of the base angle (α), calculate using the theorem of projections. From this it follows that the desired value is equal to two lengths of the sides multiplied by the cosine of the known values: b = 2*a*cos(α).

2

If the conditions the previous step to replace the angle adjacent to the base, the angle lying opposite to it (β), calculate the length of this side (b) you can use the size of the sides (a) and the other trigonometric function is the sine of half the angle. These two values multiply and double: b = 2*a*sin(β/2).

3

For the same initial data as in the previous step, there is another formula, but it also trigonometric functions includes the root. If you are not afraid, subtract from unity the cosine of the angle at the vertex of the triangle double the value obtained, extract from the root of the result and multiply it by the length of the sides: b = a*√(2*(1-cos(β)).

4

Knowing the length of the perimeter (P) and lateral side (a) of an isosceles triangle to find the length of base (b) is very easy - just subtract the first two values of the second: b = P-2*a.

5

The area value (S) of such a triangle is also possible to calculate the length of the base (b), if the known height (h) of the figure. This double square is divide by the height: b = 2*S/h.

6

Height (h) is omitted on the basis of (b) an isosceles triangle can be used to calculate the length of this side in combination with the length of the sides (a). If these two parameters are known, the lift height in the square, subtract from the obtained values of the squared lengths of the sides, from the result extract the square root, and double: b = 2*√(h2-a2).

7

Can be used to calculate the length of the base (b) and the radius (R) of a triangle circumscribed about a circle if you know the angle lying opposite the base (β). Deuce multiply by the radius and the sine of that angle: b = 2*R*sin(β).

# Advice 2 : How to calculate the length of triangle side

To calculate lengths of sides in an arbitrary triangle most often has to apply the theorem of sines and cosines. But among the whole set of arbitrary polygons of this kind there are of them "more correct" variations - equilateral, isosceles, rectangular. If the triangle is known that it belongs to one of these species, methods of calculation of its parameters is much easier. When calculating the lengths of their sides is often possible to do without trigonometric functions.

Instruction

1

**The length of the**

**side**(A) of an equilateral

*triangle*to find the radius of the inscribed circle (r). To do so, increase it to six times and divide by the square root of triples: A = r*6/√3.

2

Knowing the radius of the circumscribed circle (R), too it is possible to calculate the length of

**side**(A) right*triangle*. This radius is twice that used in the previous formula, so triple it and also divide by the square root of triples: A = R*3/√3.3

The perimeter (P) of an equilateral

*triangle*to calculate the length of its**side**(A) is even simpler, because the lengths of the sides in this figure are the same. Just divide the perimeter into three pieces: A = R/3.4

In an isosceles triangle the calculation of the length

**of the sides**of known perimeter is a bit more complicated - you need to know more and a length of at least one of the parties. If you know the length**of side**A lying in the base of the figure, the length of any side (In) find halving the difference between the perimeter (P) and the size of the base: B = (R-A)/2. And if you know the side, the length of the base define by subtracting from the perimeter to twice the length of the side: A = R-2*V.5

Knowledge area (S) occupied on the plane right triangle, is also sufficient for finding the lengths of its

**sides**(A). Extract the square root of the area ratio and the square root of three, and the result double A = 2*√(S/√3).6

In a right triangle, unlike any other, to calculate the length of one of the parties is sufficient to know the lengths of the other two. If the target side is the hypotenuse (C), to do this, find the square root of the sum of the lengths of the known sides (A and b) squared: C = √(A2+B2). But if you want to calculate the length of one of the other two sides, then the square root must be obtained from the difference of the squares of the lengths of the hypotenuse and another side: A = √(C2-B2).

# Advice 3 : How to calculate side of isosceles triangle

Isosceles, or isosceles called triangle whose lengths of two sides of the same. If necessary, calculate the length of one of the sides of such figures it is possible to use knowledge of angles at its vertices, in combination with the length of one side or radius of the circumscribed circle. These parameters of the polygon are linked by a theorem of sines, cosines, and some other permanent ratio.

Instruction

1

To calculate the length of the sides of an isosceles triangle (b) according to the known conditions of the length of its base (a) and the value of the adjacent angle (α) use the theorem of cosines. It implies that you should divide the length of the known sides for twice the cosine is given in terms of angle: b = a/(2*cos(α)).

2

The same theorem and apply for the reverse operation - calculate the length of the base (a) at a known length of sides (b) and value of angle (α) between these two parties. In this case, the theorem allows to obtain the equality, the right part of which contains twice the product of the lengths of the known sides into the cosine of the angle: a = 2*b*cos(α).

3

If in addition the lengths of the sides (b) in terms of the magnitude of the angle between them (β), to calculate the length of the base (a) use the theorem of sines. It implies a formula, according to which should be twice the length of the side multiplied by the sine of half of the known angle: a = 2*b*sin(β /2).

4

The theorem of sines can be used to find the length of the lateral side (b) of an isosceles triangle if the known base length (a) and opposite him the value of angle (β). In this case, double the sine of half of the known angle divided by the resulting value of the length of the base: b = a/(2*sin(β/2)).

5

If the isosceles triangle circumscribed circle, the radius of which (R) is known, to calculate the lengths of the sides need to know the measure of the angle at one vertex of the shape. If the conditions given information about the angle between the sides (β), calculate the length of the base (a) of the polygon by doubling the product of the radius by the sine of this angle: a = 2*R*sin(β). If given the value of the base angle (α) to find the length of the lateral side (b) just replace the angle in the formula: b = 2*R*sin(α).