If you know one acute angle and one of the three sides, you can find the other acute angle and the other two sides.If you know two of the three sides, you can find the third side and both acute angles.Besides these, there’s the all-important Pythagorean formula that says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.Īlong with the knowledge that the two acute angles are complementary, that is to say, they add to 90°, you can solve any right triangle: These three formulas are collectively known by the mnemonic SohCahToa. If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side. The most important formulas for trigonometry are those for a right triangle. The area of the sector is half the square of the radius times the angle, where, again, the angle is measured in radians. To convert from degrees to radians, multiply the number of degrees by π/180.Īrea of a sector.
The length of the arc is just the radius r times the angle θ where the angle is measured in radians. You can easily find both the length of an arc and the area of a sector for an angle θ in a circle of radius r. The identities don’t refer to particular geometric figures but hold for all angles. These formulas relate lengths and areas of particular circles or triangles.
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