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Geometry
Level
pending
If then find A (in degrees).
Note: Assume
The answer is 20.51.
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1 solution
if :sin(A)+sin(A+20)=1 therefore, sin(A)+sin(a)cos(20)+cos(A)sin(20)=1
sin(A)(1+cos(20))+cos(A)sin(20)=1
then we know that ,
cos(20)=(2cos(10)^2) -1 , sin (20)=2sin(10)cos(10)
therefore,
sin(A)cos(10)^2 +2sin(10)cos(10)=1
2cos(10)*(sin(A)cos(10)+cos(A)sin(10))=1
we know, sin(a+10)=(sin(A)cos(10)+cos(A)sin(10)
then, 2cos(10)sin(A+10)=1
sin(A=10)=0.577
then, A+10=30.51 A=20.51
OR A+10=149.489 A=139.489
the condition says that" A cannot be more than 90 or less than 0"
Finally we have A=20.51 .