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2. Law of sines - Wikipedia

   en.wikipedia.org/wiki/Law_of_sines

   In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

3. Spherical trigonometry - Wikipedia

   en.wikipedia.org/wiki/Spherical_trigonometry

   The sine rule gives C and then we have Case 7. There are either one or two solutions. Case 4: two angles and an included side given (ASA). The four-part cotangent formulae for sets (cBaC) and (BaCb) give c and b, then A follows from the sine rule. Case 5: two angles and an opposite side given (AAS). The sine rule gives b and then we have Case 7 ...

4. Solution of triangles - Wikipedia

   en.wikipedia.org/wiki/Solution_of_triangles

   For the spherical case, one can first compute the length of side from the point at α to the ship (i.e. the side opposite to β) via the ASA formula ⁡ = ⁡ ⁡ ⁡ (+) + ⁡ ⁡ (), and insert this into the AAS formula for the right subtriangle that contains the angle α and the sides b and d: ⁡ = ⁡ ⁡ = ⁡ + ⁡ ⁡. (The planar ...

5. Sine and cosine - Wikipedia

   en.wikipedia.org/wiki/Sine_and_cosine

   In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...

6. Trigonometry - Wikipedia

   en.wikipedia.org/wiki/Trigonometry

   Given two sides a and b and the angle between the sides C, the area of the triangle is given by half the product of the lengths of two sides and the sine of the angle between the two sides: [85] Area = Δ = 1 2 a b sin ⁡ C {\displaystyle {\mbox{Area}}=\Delta ={\frac {1}{2}}ab\sin C}

7. PayPal fixes outage that affected thousands worldwide - AOL

   www.aol.com/news/paypal-outage-affects-thousands...

   The company experienced a system issue that affected multiple products including account withdrawals, peer-to-peer payment service Venmo, online checkout and crypto. PayPal said the issue, which ...

8. List of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/List_of_trigonometric...

   Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

9. 10 Classic Southern Holiday Recipes To Make Right Now

   www.aol.com/10-classic-southern-holiday-recipes...

   2. Hoppin’ John. Southerners are usually eating Hoppin’ John (a simmery mix of black-eyed peas and rice) on New Year's Day. Like most “vegetable” recipes from around this area, it contains ...