How To Find The Angle Of A Triangle If We Know The Two Sides? | Education

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# How to find the angle of a triangle if we know the two sides?

In a right triangle, you can simply find a corner, if you know two of its sides. One of the corners is 90 degrees and the other two are always acute. These angles and will need to find. To find an acute angle in a right triangle, it is necessary to know the values ​​of all three of its sides. Depending on what side you know, sinuses sharp corners can be found using the formulas for trigonometric functions. four digit mathematical table used for finding the sine of the angle at.

### You will need:

- Pythagorean theorem; - Trigonometric function sin; - Four-mathematical Bradis table.

## Instruction how to find the angle of a triangle if we know the two sides?

Step 1:

Use the following notation for the convenience of drawing up the formulas necessary for calculations: c - the hypotenuse of a right triangle; a, b - the legs of which form a right angle; A - an acute angle opposite leg b; B - acute angle opposite leg a.

Step 2:

Calculate what is the length of the unknown side of the triangle. Apply for calculations Pythagorean theorem. Calculate the leg of a, if the values ​​of the hypotenuse c and the leg b. To do this, subtract the square of the hypotenuse c square leg b, then calculate the square root of the result.

Step 3:

Calculate the leg b, if the values ​​of the hypotenuse c and the leg a. To do this, subtract the square of the hypotenuse c square leg a, and then calculate the square root of the result.

Step 4:

Calculate the hypotenuse c, if we know the two leg. To do this, you get the sum of the squares of the legs a and b, then calculate the square root of the result and rounded to four decimal places, if necessary.

Step 5:

Calculate the sine of the angle A formula sinA = a / c. Use the calculator for calculations. Round if necessary the sine of the angle A to four decimal places.

Step 6:

Calculate the sine of the angle B from the formula sinB = b / c. Use the calculator for calculations. Round if necessary the sine of the angle B to four decimal places.

Step 7:

Find the angles A and B from the values ​​of their sinuses. Use this to determine the values ​​of the angles table VIII of the four-Bradis mathematical tables. Find the values ​​in the table of sines. Walk on the left and the value found in the first column "A", take degrees. Move on up and found values ​​of "A" top of the line, take a minute. For example, if sin (A) = 0,8949, the angle A is 63 degrees 30 minutes.