Advice 1: How to find the hypotenuse, knowing a side and angle

There are many types of triangles: right, isosceles, acute-angled, and so on. They all have unique properties to them and each has its own rule for finding a value, whether it is side or base angle. But because of the variety of these geometric figures in a separate group can be distinguished triangle with a right angle.
How to find the hypotenuse, knowing a side and angle
You will need
  • A clean sheet, a pencil and a ruler to the diagram of the triangle.
Instruction
1
The triangle is rectangular if one of its angles equal to 90 degrees. It consists of two legs and a hypotenuse. The hypotenuse is called the great side of this triangle. It lies against the straight edge. The other two sides, respectively called the lower side of it. They can be equal and have different values. The equality of the legs means that you are working with an isosceles right triangle. The beauty of it is that it combines the properties of two shapes: rectangular and isosceles triangle. If the legs are not equal, then the triangle is arbitrary and obeys the basic law: the greater the angle, the more lying in front of him roll.
2
There are several ways of finding the hypotenuse leg and angle. But before you use one of them, you should determine what side and angle known. If given an angle and adjacent to it side, then the hypotenuse will be easier to find the cosine of the angle. The cosine of an acute angle (cos a) in a right triangle is the ratio of the adjacent leg to the hypotenuse. It follows that the hypotenuse (C) is equal to the ratio of adjacent sides (b) to the cosine of angle a (cos a). This can be written as: cos a=b/c => c=b/cos a.
3
If given angle and opposite side, it is necessary to work with the sine. The sine of an acute angle (a sin) in a right triangle is the ratio of the opposite leg (a) to the hypotenuse (c). There is a principle that in the previous example, but instead of cosine functions taken sinus. sin a=a/c => c=a/sin a.
4
You can also use a trigonometric function such as tangent. But finding unknown values is slightly more complicated. The tangent of an acute angle (tg a) in a right triangle is the ratio of the opposite leg (a) surrounding (b). Finding both of the leg, apply the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the other two sides) and a large side of the triangle will be found.
Note
Working with the Pythagorean theorem, do not forget that you are dealing with a degree. Finding the sum of the squares of the other two sides, to obtain the final answer should be square root.

Advice 2: 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.
How to find the hypotenuse on the side and corners
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.
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