Finding area of triangles. Area of a triangle Law of sines Trig ratios are generally used to find unknown measures in right triangles, but they can also.

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Presentation transcript:

Finding area of triangles

Area of a triangle

Law of sines Trig ratios are generally used to find unknown measures in right triangles, but they can also be used to find unknown lengths in any triangle using the Law of Sines.

Law of Sines In any triangle, RST a = b = c sinA sinB sinC B C A a c b

Finding distance using Law of Sines Find the length of x. Round to nearest hundredth.

Find the distances b and c 4.56 = c Sin43 Sin = b Sin 43 Sin 80

Possible triangles The length of the side opposite the given angle must be greater than the height but less than the length of the other given side see p. 507

Finding measure of an angle using Law of Sines AB = AC SinC Sin B 12 = 14 SinC Sin 75 14SinC = 12Sin75 SinC = 12Sin75 14 C = sin -1 (12sin75) 14 C = 56 o 180 -(56+75) = A= 49 o = 12 =14 =75 o

Find the measure of angle x to the nearest degree Find <Y first, then <X X Y Z o

Find the length of TU to the nearest hundredth 108 o 31 o T U V 110

Find <D and < E to the nearest degree o D E F

Marissa and Hector walk away from each other on straight paths that make a 66 degree angle with each other. When they stop, Hector is 125 feet away from the starting point, and he is 120 feet away from Marissa. How far did Marissa walk, to the nearest foot?