Step-by-step explanation:
Given
sin theta = 12/ 13 = p/h
Therefore p = 12 , h = 13 and b = ?
We know by using Pythagoras theorem
b² = h² - p²
b² = 13² - 12²
b² = 169 - 144
b² = 25
b² = 5²
Therefore b = 5
So now
cos theta
= b/h
= 5 / 13
The value of cosθ is [tex]\frac{5}{13}[/tex]
'The cosine of an angle is defined as the sine of the complementary angle. The complementary angle equals the given angle subtracted from a right angle, 90°.'
According to the given problem,
We know, in a right angle triangle,
sinθ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
Given, sinθ = [tex]\frac{12}{13}[/tex]
⇒ Perpendicular = 12
⇒ Hypotenuse = 13
Applying Pythagoras theorem,
Hypotenuse² = Perpendicular² + Base²
⇒ 13² = 12² + Base²
⇒ Base² = 13² - 12²
⇒ Base = √( 13² - 12²)
⇒ Base = 5
We know, cosθ = [tex]\frac{Base}{Hypotenuse}[/tex]
⇒ cosθ = [tex]\frac{5}{13}[/tex]
Hence, we can conclude, the value cosθ is [tex]\frac{5}{13}[/tex]
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