Similarly, the law of cosines is appropriate when two sides and an included angle are known or three sides are known. For example, the law of sines is employed when two angles and a side are known or when two sides and an angle opposite one are known. To solve a triangle, all the known values are substituted into equations expressing the laws of sines and cosines, and the equations are solved for the unknown quantities. The law of sines is expressed as an equality involving three sine functions while the law of cosines is an identification of the cosine with an algebraic expression formed from the lengths of sides opposite the corresponding angles. To secure symmetry in the writing of these laws, the angles of the triangle are lettered A, B, and C and the lengths of the sides opposite the angles are lettered a, b, and c, respectively. Triangles can be solved by the law of sines and the law of cosines. If enough sides and angles are known, the remaining sides and angles as well as the area can be calculated, and the triangle is then said to be solved. In many applications of trigonometry the essential problem is the solution of triangles. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.
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