In a right-angled triangle, one of the legs is equal to b, and the angle opposite to it is equal to a. Express the second leg, the adjacent acute angle, and the hypotenuse through b and a.
The second unknown leg is adjacent to the corner a. The tangent of angle a is equal to the ratio of the opposite leg in to the adjacent unknown leg. Then the leg will be equal to the ratio of the leg b to the tangent of the angle a;
Since the sine of the angle a is equal to the ratio of the opposite leg b to the hypotenuse, then the hypotenuse can be expressed through the ratio of the leg b to the sine of the angle a;
Since the sum of all the angles of the triangle is 180 °, the unknown acute angle will be equal to the difference: 180 ° – 90 ° right angle – angle a.
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