Question

A sin theta = 3 and A cos theta = 4 then what is A?​

Answer 1

Answer:

a = ±5

Step-by-step explanation:

$a \sin( \theta) = 3 \: \: \: .............(1) \\ a \cos( \theta ) = 4 \: \: \: \: .................(2) \\ squaring \: and \: adding \: (1) \: and \: (2) \\ {a}^{2} { sin }^{2}( \theta) + {a}^{2} ({cos})^{2} ( \theta) = 25 \\ {a}^{2} ( {sin}^{2} ( \theta) + {cos}^{2} (\theta)) = 25 \\ {a}^{2} = 25 \\ = > \fbox{a = ±5}$

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Answer 2

Let theta = x

A sin(x) = 3 ........(1)

A cos(x) = 4 ............(2)

squaring and adding 1 and 2.

A^2 = 25

=> A = ±5