The Law

of Sines Right Angle Triangle a right angle triangle has a 90° angle This is an acute angle triangle all angles are less than 90° Can you use the trig ratios now? of course because we have a right angle! What about triangles that do not have a right angle? Remember these three trigonometric identities? Let's label the triangle Did you get this? Sin(B)=h/c Re-arrange to solve for h Did you get this?

sinC/c = sinB/b Write a sine ratio for angle B Did you get this? sin(C) = opp/hyp

cos(C)=adj/hyp

tan(C)=opp/adj sin(C) = opp/hyp= c/b

cos(C)=adj/hyp=a/b

tan(C)=opp/adj=c/a Draw line h Draw a straight line from angle B to side b Write a sine ratio for angle A and angle C Re-arrange your expressions like you did previously so you get one expression Let's give it a try!! sinC/c = sinA/a sinA/a = sinB/b = sinC/c This is the law of sines Find side length a Let's solve this together! sinB/b = sinA/a sin(50° )/4=sin(75° )/a 0.766/4=0.966/a 0.1915=0.966/a a(0.1915)=0.966 a=5.04cm What about an obtuse triangle? Find all the missing angles and side lengths Let's find side b sinA/a = sinB/b sin(120°)/82=sin(38°)/b 0.866/82=0.6157/b (0.01056)b=0.6157 b=58.30mm We need angle C and side C angle C = 180°-120° -38° Let's find side C sinA/a = sinC/c You just learned the law of sines! Next lesson we'll look at ambiguous

cases! Do the same thing for angle C? Sin(C)=h/b c=35.47mm angle C = 22° sin(120°)/82=sin(22°)/c 0.01056=(0.3746)/c 0.01056=0.6157/b 0.8660/82=0.3746/c a/sinA = b/sinB = c/sinC Can also be written like this or

c/Sinc = b/sinB or

c/sinC = a/sinA MS. Romo

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