How To Find If You Know The Hypotenuse Of A Leg And The Angle | The Science

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# How to find if you know the hypotenuse of a leg and the angle

In the right-angled triangle is called the leg side, adjacent to the right angle and the hypotenuse - the side opposite the right angle. All sides of a right triangle are linked by certain relations, and it is these constant relations will help us to find the hypotenuse of a right triangle by any known leg and a corner.

### You will need:

Paper, Pen, table of sines (available online)

## Instruction how to find the hypotenuse and a leg if you know the angle

Step 1:

We denote sides of a right triangle small letters a, b and c, and the angles opposite to them, respectively, A, D and C. Suppose known cathetus opposite to it and a corner A.

Step 2:

Then, we find the sine of angle A. To do this, find the sine table value corresponding to the specified angle. For example, if the angle A is 28 degrees, then its sine equal to 0.4695.

Step 3:

Knowing leg and a sine of the angle A, we find the hypotenuse, leg and divided by the sine of the angle A. (c = a / sin A). The meaning of this action would be understandable if we recall that the sine of the angle A - is the ratio of the opposite leg (a) to the hypotenuse (c). That is, sin A = a / s, and from this equation is easily derived formula we just used.

Step 4:

If you know a leg and an adjacent angle B, then before proceeding with steps 2 and 3, we find the angle A. For this purpose, from 90 (in the right-angled triangle the sum of acute angles is 90 degrees), subtract the value of the known angle. That is, if we know the angle has a measure of 62-degree, 90 - 62 = 28, ie the angle A is equal to 28 degrees. Calculating the angle A, simply repeat the steps outlined in steps 2 and 3, and we obtain the length of the hypotenuse c.