How to find the angle of a right triangle

The first methods for finding the unknown parameters of various, including rectangular, triangles were developed by scientists of ancient Greece, several centuries BC. Greek astronomers did not consider sines, cosines, and tangents. These concepts were introduced by Indian and Arab scholars in the Middle Ages.

You will need

calculator or table of natural values ​​of trigonometric functions.

Instruction manual

one

The trigonometric functions of acute angles can be defined as the ratio of the lengths of the sides of a right triangle.

Sine: sin? = a / c = opposite leg / hypotenuse

Cosine: cos? = b / s = adjacent leg / hypotenuse

Tangent: tan? = sin? / cos? = a / b = opposite leg / adjacent leg

Cotangent: cot? = cos? / sin? = b / a = adjacent leg / opposite leg

2

The sum of the angles of any triangle is 180 °, that is? +? +? = 180 °. Since in a right triangle one of the angles (in our case, the angle?) Is always equal to 90 °, the equality +? = 90 ° or? = 90 ° -?, ? = 90 ° -?.

3

If we know side a (opposite leg) and side c (hypotenuse), then the angles of the triangle? and? can be found as follows. Knowing that the ratio of the opposite leg to the hypotenuse c is the sine of the angle?, Then dividing a by c we get sin ?. Further, according to the special tables “Natural values ​​of sin? We find the angle?. For example, sin? = 0.5 then the angle? Is 30 °. The value of the second angle is? = 90 ° -?

4

If we know side b (adjacent leg) and side c (hypotenuse), then dividing b by c we get cos ?. Further, according to the table or using a calculator, we determine the angle?. For example cos? = 0.7660, then the angle? equal to 50 °, therefore, the angle? = 90 ° - 50 ° = 40 °.

5

If we know side a (opposite side) and side b (adjacent side), then dividing, and by b we get the value tan ?. Further on the table or using the calculator we find the value of the angle itself. For example, if tan? = 0.8391, then the angle? = 40 °, therefore, the angle? = 90 ° - 40 ° = 50 °