You will need

- Paper, pen, table of sines (in the Internet)

Instruction

1

We denote the sides of a right triangle by the small letters a, b, and c and angles opposite them, respectively, And, And C. and Suppose known side and opposite him the angle A.

2

Then find the sine of the angle A. To do this, the table of sines we find the value for a given corner. For example, if the angle A is 28 degrees, its sine is 0.4695.

3

Knowing the other two sides and the sine of the angle A, find the hypotenuse, dividing side a by the sine of angle A. (c = a/sin A). The meaning of this action becomes intelligible if we remember that the sine of an angle And it's opposite leg to the hypotenuse (C). That is, sin A=a/C, and this equation is easily derived formula we just used.

4

If you know a leg and the adjacent angle, then before you begin any of the steps 2 and 3, find the angle A. To do this, from 90 (in a right triangle the sum of the acute angles is 90 degrees) subtract the value of a known angle. That is, if we know the angle has degree measure 62, the 90 - 62 = 28, that is, the angle A is 28 degrees. Calculating the angle And just repeat the steps in steps 2 and 3, and get the length of the hypotenuse C.

Useful advice

If a right triangle has an acute angle of 30 degrees, then opposite it is the side whose length is 2 times smaller than the length of the hypotenuse.

# Advice 2: How to find the hypotenuse in a right triangle

Call the hypotenuse side in a right triangle that lies opposite the right angle. The hypotenuse is the longest side in a right triangle. The other sides in a right triangle are called legs.

You will need

- Basic knowledge of geometry.

Instruction

1

The squared length of the hypotenuse equals the sum of the squares of the other two sides. That is, to find the square of the length of the hypotenuse you need to square the lengths of the legs and fold.

2

The length of the hypotenuse is equal to the square root of the square of its length. To find its length, extract the square root of the number equal to the sum of the squares of the legs. The resulting number will be the length of the hypotenuse.

Note

The length of the hypotenuse is a positive value, therefore, when extracting the root, radical expression must be greater than zero.

Useful advice

In an isosceles right triangle the length of the hypotenuse can be calculated by multiplying the leg to the root of the two.

# Advice 3: How to find the hypotenuse on the side and corners

Is called the hypotenuse side in a right triangle that is opposite the angle of 90 degrees. In order to calculate its length, enough to know the length of one of the legs and the size of one of the acute angles of the triangle.

Instruction

1

At a known side and an acute angle of a right triangle, the hypotenuse can be equal to the ratio of the leg to the cosine/sine of that angle if the given angle is opposite him/yard:

h = C1(or C2)/sinα;

h = C1(or C2)/cosα.

Example: suppose that we are given right triangle ABC with hypotenuse AB and a right angle C. Let angle B equal 60 degrees, and angle a of 30 degrees Length of side BC is 8 cm Need to find the length of the hypotenuse AB. For this you can use any of the above methods:

AB = BC/cos60 = 8 cm.

AB = BC/sin30 = 8 cm.

h = C1(or C2)/sinα;

h = C1(or C2)/cosα.

Example: suppose that we are given right triangle ABC with hypotenuse AB and a right angle C. Let angle B equal 60 degrees, and angle a of 30 degrees Length of side BC is 8 cm Need to find the length of the hypotenuse AB. For this you can use any of the above methods:

AB = BC/cos60 = 8 cm.

AB = BC/sin30 = 8 cm.

# Advice 4: How to determine angles in a right triangle

The rectangular triangle is characterized by certain relationships between the angles and sides. Knowing the meaning of some of them, you can calculate the other. For this purpose, formula, based, in turn on the axioms and theorems of geometry.

Instruction

1

From the name of a right triangle it is clear that one of its angles is a direct. Regardless of whether it is an isosceles right triangle or not, it always has one angle equal to 90 degrees. If given a right triangle that is both isosceles and then, based on the fact that the figure is a straight angle, find two angles at its base. These angles are equal, so each of them has a value equal to:

α=180°- 90°/2=45°

α=180°- 90°/2=45°

2

In addition to the above, it is also possible the other case, when the triangle is rectangular, but is not isosceles. In many problems the angle of the triangle is 30° and the other 60°, because the sum of all angles in a triangle must equal 180°. If given the hypotenuse of a right triangle and side angle can be found from matching the two sides:

sin α=a/c where a is the side opposite to the hypotenuse of a triangle, with the hypotenuse of the triangle

Accordingly, α=arcsin(a/c)

Also the angle you can find the formula for cosine:

cos α=b/c where b is the adjacent side to the hypotenuse of the triangle

sin α=a/c where a is the side opposite to the hypotenuse of a triangle, with the hypotenuse of the triangle

Accordingly, α=arcsin(a/c)

Also the angle you can find the formula for cosine:

cos α=b/c where b is the adjacent side to the hypotenuse of the triangle

3

If you know only two sides, the angle α can be found according to the formula of the tangent. The tangent of this angle is equal to the ratio of opposite over adjacent:

tg α=a/b

From this it follows that α=arctg(a/b)

When the straight angle and one of the corners found by the above method, the second is as follows:

ß=180°-(90°+α)

tg α=a/b

From this it follows that α=arctg(a/b)

When the straight angle and one of the corners found by the above method, the second is as follows:

ß=180°-(90°+α)

# Advice 5: How to calculate the hypotenuse in a right triangle

If one of the angles in a triangle is equal to 90°, then the two adjacent sides can be called the legs, and the triangle is rectangular. The third side in this figure is called the hypotenuse, and its length is associated with, perhaps, known on the planet a mathematical postulate - the Pythagorean theorem. However, to calculate the length of this side, you can use it.

Instruction

1

The Pythagorean theorem use to find the length of the hypotenuse (C) of a triangle with known values of both legs (a and b). You need to put their sizes in square and folded, and the result extract the square root: c = √(a2+b2).

2

If the sizes of both of the other two sides (a and b) in terms of the given height (h), descended on the hypotenuse (c), the need for the calculation of degrees and roots will disappear. Multiply the length of the shortest sides and divide the result by the height: c = a*b/h.

3

At known values of the angles at the vertices of a right triangle adjacent to the hypotenuse and length of one of the other two sides (a), use the definitions of trigonometric functions - sine and cosine. Choosing one of them depends on the mutual arrangement of the known side and is involved in the calculation of the angle. If the leg is opposite the angle (α), so from the definition of the sine is the length of the hypotenuse (c) must be equal to the product of the length of this leg to the sine of the opposite angle: c = a*sin(α). If involved angle (β), which is adjacent to the known side, use the definition of cosine multiply the length of the side adjacent to the cosine of the angle: c = a*cos(β).

4

Knowledge of the radius (R) circumscribed about the right triangle circumference makes the calculation of the length of the hypotenuse (c) is a very simple task - just increase this value twice: c = 2*R.

5

The median, by definition, bisects the side to which it is omitted. As follows from the previous step, half of the hypotenuse is equal to the radius of the circumscribed circle. Since the vertex on the hypotenuse may be omitted median, also have to lie on the circumscribed circle, the length of this cut equal to the radius. So, if the length of the median (f) omitted from the right angle, is known, to calculate the size of the hypotenuse (c) you can use a formula similar to the previous one: c = 2*f.