SOLUTION: If the tangent ratio of an acute angle is 0.75 (ie Tan a=0.75 ), while the tangent ratio of another acute angle is 2.4 (ie tan b=2.4 ), find the exact value of sin(a-b). You may

Question 888381: If the tangent ratio of an acute angle is 0.75 (ie Tan a=0.75 ), while the tangent ratio of another acute angle is 2.4 (ie tan b=2.4 ), find the exact value of sin(a-b). You may not use the tan inverse feature of your calculator for this question.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If the tangent ratio of an acute angle is 0.75 (ie Tan a=0.75 ), while the tangent ratio of another acute angle is 2.4 (ie tan b=2.4 ), find the exact value of sin(a-b)
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Find the sin and cos of angles a and b
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Using a 3-4-5 triangle
tan(A) = 3/4
sin(A) = 3/5
cos(A) = 4/5
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Using a 5-12-13 triangle
tan(B) = 2.4 = 12/5
sin(B) = 12/13
cos(B) = 5/13
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sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
= (3/5)*(5/13) - (4/5)*(12/13)
= 3/13 - 48/65
= -33/65
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