Monday, May 27, 2013

Madison and Brandons Unit 3 Day 6 Blog(Trigonometry)

Unit 3, Day 6: Objective: Non right triangle trig: Law of Sines, Law of Cosines, Area of a triangle.

Define: In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. The law of sines works for any triangle even if the triangle does not contain a 90 degree angle. The law of cosine relates the lengths of the sides of a plane triangle to the cosine of one of its angles. The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known. The area of a triangle is the amount of space a triangle covers.


\frac{\sin A}{a} \,=\, \frac{\sin B}{b} \,=\, \frac{\sin C}{c} \!                                             \frac{a}{\sin A} \,=\, \frac{b}{\sin B} \,=\, \frac{c}{\sin C} \,=\, D \!
 

 
 The law of cosines says where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c.
c^2 = a^2 + b^2 - 2ab\cos\gamma\,
 
By changing which sides of the triangle play the roles of a, b, and c in the original formula, one discovers that the following two formulas also state the law of cosines:
a^2 = b^2 + c^2 - 2bc\cos\alpha\,
b^2 = a^2 + c^2 - 2ac\cos\beta.\,
 
 
 
 

 
 
 
 
 
 
 

Quiz:



 Answer Key:



 
 
 
 
 
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