In a right triangle, we know that the sine of one angle is equal to the cosine of its complementary angle. Therefore, we can use the relationship \(\sin\theta = \cos(90^\circ - \theta) = \cos\phi\) in this case.
Given:
\[ \cos\phi = x + 0.2 \] \[ \sin\theta = 2x - 0.5 \]
Since \(\sin\theta = \cos\phi\), we can set the two equations equal to each other:
\[ 2x - 0.5 = x + 0.2 \]
Now, let's solve for \(x\).
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Subtract \(x\) from both sides: \[ 2x - x - 0.5 = 0.2 \] \[ x - 0.5 = 0.2 \]
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Add 0.5 to both sides: \[ x = 0.2 + 0.5 \] \[ x = 0.7 \]
Thus, the value of \(x\) is \(0.7\).
So the answer is:
0.7