The correct value of Sine θ is 5/13
From the question given above, the following data were obtained:
Cos θ = 12/13
Sine θ =?
Next, we shall determine the opposite. This can be obtained as follow:
[tex]Cos \theta = \frac{Adjacent}{Hypothenus}\\\\Cos \theta = \frac{12}{13}[/tex]
Adjacent = 12
Hypothenus = 13
Opposite =?
Hypothenus² = Opposite² + Adjacent²
13² = Opposite² + 12²
169 = Opposite² + 144
Collect like terms
169 – 144 = Opposite²
25 = Opposite²
Take the square root of both side
Opposite = √25
Opposite = 5
Finally, we shall determine the Sine θ. This can be obtained as follow:
Opposite = 5
Hypothenus = 13
Sine θ =.?
[tex]Sine\theta = \frac{Opposite}{Hypothenus}\\\\Sine\theta = \frac{5}{13}[/tex]
Therefore, the value of Sine θ is 5/13
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