[tex]S\frac{O}{H} C\frac{A}{H} T\frac{O}{A}[/tex]
or in other words
[tex]Sin\frac{opposite}{hypotenuse} Cos\frac{adjacent}{hypotenuse} Tan\frac{opposite}{adjacent}[/tex]
3 is the opposite, and 5 is the hypotenuse.
You can use the pythagorean theorem to find the other side(adjacent)
a²+b²=c²
3²+b²=5²
9+b²=25 Subtract 9 on both sides
b²=16 Square root both sides
b = √16
b = 4
So the adjacent is 4.
tan theta = opposite/adjacent
tan theta = 3/4
In trigonometry sin theta is the ratio of the opposite side to the hypotenuse side.The value of the tan theta is 3/4.
The value of the sin theta given in the question is,
[tex]sin\theta=\dfrac{3}{5}[/tex]
In trigonometry sin theta is the ratio of the opposite side to the hypotenuse side.
Let [tex]a[/tex] is the adjacent side, [tex]b[/tex] is the opposite side and [tex]c[/tex] is the hypotenuse side. Thus the value of the sin theta;
[tex]sin\theta=\dfrac{b}{c}[/tex]
The given value of the sin theta in the question is,
[tex]sin\theta=\dfrac{3}{5}[/tex]
When we equate both the values of the sin theta we get, [tex]b[/tex] is 3 and [tex]c[/tex] is 5.
According to the Pythagoras theorem;
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+3^2=5^2[/tex]
[tex]a^2=25-9[/tex]
[tex]a=\sqrt{16} =4[/tex]
In trigonometry tan theta is the ratio of the opposite side to the adjacent side.Thus,
[tex]tan \theta=\dfrac{c}{a}[/tex]
[tex]tan \theta=\dfrac{3}{4}[/tex]
Thus the value of the tan theta is 3/4.
Learn more about the trigonometry follow the link below-
https://brainly.com/question/13710437
