Given that sin(2x+10)=cos(3x+40), find the number of degrees in the acute angles of the corresponding right triangle.
Answers
Answered by
5
Since cos A = sin(90-A)
cos(3x+40)=sin(90°-(3x+40))
=sin(50-3x)
From the given equation
sin(2x+10)=cos(3x+40)
sin(2x+10)=sin(50-3x)
On equating the arguments,
2x+10=50-3x
5x=40°
x=8°
cos(3x+40)=sin(90°-(3x+40))
=sin(50-3x)
From the given equation
sin(2x+10)=cos(3x+40)
sin(2x+10)=sin(50-3x)
On equating the arguments,
2x+10=50-3x
5x=40°
x=8°
lovingt:
That's what I had at first but then there is multiple choice answers of 20 and 70, 25 and 65, 26 and 64 or 30 and 60. I'm just really confused of what I have to do.
Try substitution... best method of all time.
OH I understand now! Thank you!!
Answered by
8
Hello !
See,
sin(90-A)= cos (A) or sin A = cos (90 - A)
Putting this equation in the following question we get that ,
sin ( 2x + 10 ) = sin ( 90 - 3x - 40 )
⇒ 2x +10 = 50 - 3x
⇒ 5 x = 40
⇒ x = 40 / 5
⇒ x = 8°
Now substituting the value of x in the question we get ,
sin ( 2×8+10) = cos ( 3×8 + 40)
⇒ sin ( 26°) = cos ( 64°)
I hope this answer is correct !
Please mark this answer as the best !
Thank you!
See,
sin(90-A)= cos (A) or sin A = cos (90 - A)
Putting this equation in the following question we get that ,
sin ( 2x + 10 ) = sin ( 90 - 3x - 40 )
⇒ 2x +10 = 50 - 3x
⇒ 5 x = 40
⇒ x = 40 / 5
⇒ x = 8°
Now substituting the value of x in the question we get ,
sin ( 2×8+10) = cos ( 3×8 + 40)
⇒ sin ( 26°) = cos ( 64°)
I hope this answer is correct !
Please mark this answer as the best !
Thank you!
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