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A triangle can be uniquely determined in this sense when given any of the following: [1] [2] Three sides (SSS) Two sides and the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA)
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
A right triangle with the hypotenuse c. In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. [7] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem.
The opposite side is the side opposite to the angle of interest; in this case, it is . The hypotenuse is the side opposite the right angle; in this case, it is . The hypotenuse is always the longest side of a right-angled triangle. The adjacent side is the remaining side; in this case, it is . It forms a side of (and is adjacent to) both the ...
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees). The side opposite to the right angle is called the hypotenuse (side in the figure).
In similar triangles, the ratios of the sides are the same regardless of the size of the triangles, and depend upon the angles. Consequently, in the figure, the triangle with hypotenuse of unit size has opposite side of size sin θ and adjacent side of size cos θ in units of the hypotenuse.
The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. See below under Mnemonics. Sine (denoted sin), defined as the ratio of the side opposite the angle to the hypotenuse.
Image mnemonic to help remember the ratios of sides of a right triangle. The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English: Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent