If a sin theta = 3 and a cos theta = 4,then a | vedclass

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(A) Given equations are:$a \sin 	heta = 3$  --- $(1)$$a \cos 	heta = 4$  --- $(2)$Squaring both equations:$(a \sin 	heta)^2 = 3^2 \implies a^2 \sin

Vedclass · Accepted Answer

$5$

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(A) Given equations are:$a \sin 	heta = 3$  --- $(1)$$a \cos 	heta = 4$  --- $(2)$Squaring both equations:$(a \sin 	heta)^2 = 3^2 \implies a^2 \sin^2 	heta = 9$  --- $(3)$$(a \cos 	heta)^2 = 4^2 \implies a^2 \cos^2 	heta = 16$  --- $(4)$Adding equations $(3)$ and $(4)$:$a^2 \sin^2 	heta + a^2 \cos^2 	heta = 9 + 16$$a^2 (\sin^2 	heta + \cos^2 	heta) = 25$Since $\sin^2 	heta + \cos^2 	heta = 1$,we have:$a^2 (1) = 25$$a^2 = 25$Since $a > 0$,we take the positive square root:$a = 5$.

If $a \sin \theta = 3$ and $a \cos \theta = 4$,then $a = \dots$ (where $a > 0$).

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