# Given that sin(2x+10)=cos(3x+40), find the number of degrees in the acute angles of the corresponding right triangle.

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by lovingt

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by lovingt

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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°

The Brainliest Answer!

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

⇒

sin ( 2×8+10) = cos ( 3×8 + 40)

⇒

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Thank you!