Respuesta :
Answer:
sin O = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
given tan O = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
Then this is a right triangle with legs 3 and 4
Using Pythagoras' identity then the hypotenuse (h ) is
h = [tex]\sqrt{3^2+4^2}[/tex] = [tex]\sqrt{25}[/tex] = 5, hence
sin O = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex]
The value of [tex]sin(\theta)[/tex] is [tex]\dfrac{3}{5}[/tex].
Given that:
[tex]tan(\theta) = \dfrac{3}{4}[/tex]
To find : value of [tex]sin(\theta)[/tex].
Calculations will go as follows:
We can either use inverse trigonometric functions to evaluate sine, but we will use simple method by using Pythagoras Theorem:
[tex]tan(\theta) = \dfrac{Perpendicular}{Base} = \dfrac{3}{4}\\[/tex]
Thus, we have:
Perpendicular = 3x,
Base = 4x, (we used x so that we cover all Perpendicular and Base such that their ratio is 3/4)
Thus, by Pythagoras Theorem, we have:
[tex]H^2 = P^2 + B^2\\H = \sqrt{(3x)^2 + (4x)^2 } = \sqrt{25x^2} = 5x[/tex]
Thus, we have:
[tex]sin(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\sin(\theta) = \dfrac{3x}{5x} = \dfrac{3}{5}[/tex]
Thus, the value of [tex]sin(\theta)[/tex] is [tex]\dfrac{3}{5}[/tex].
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