2) sin43cdot sin43=cos43cdot c=43=7

It seems there is a mistake in the equation you provided. Let's clarify the correct steps to solve this problem.<br /><br />Given:<br />\[ \sin 43^\circ \cdot \sin 43^\circ = \cos 43^\circ \cdot c = 43 = 7 \]<br /><br />First, let's correct the equation:<br />\[ \sin^2 43^\circ = \cos 43^\circ \cdot c \]<br /><br />We know that:<br />\[ \sin^2 \theta + \cos^2 \theta = 1 \]<br /><br />So,<br />\[ \sin^2 43^\circ = 1 - \cos^2 43^\circ \]<br /><br />Now, substitute this into the equation:<br />\[ 1 - \cos^2 43^\circ = \cos 43^\circ \cdot c \]<br /><br />Let \( x = \cos 43^\circ \). Then the equation becomes:<br />\[ 1 - x^2 = x \cdot c \]<br /><br />Rearrange to solve for \( c \):<br />\[ c = \frac{1 - x^2}{x} \]<br /><br />Now, we need to find the value of \( \cos 43^\circ \). Using a calculator:<br />\[ \cos 43^\circ \approx 0.735 \]<br /><br />Substitute this value back into the equation:<br />\[ c = \frac{1 - (0.735)^2}{0.735} \]<br />\[ c = \frac{1 - 0.541225}{0.735} \]<br />\[ c = \frac{0.458775}{0.735} \]<br />\[ c \approx 0.624 \]<br /><br />Therefore, the correct value of \( c \) is approximately 0.624.