The value of [tex]csc(\theta)[/tex] is [tex]\frac{15}{12}[/tex]
"It is a triangle in which one of the angle measures 90° "
"It is the longest side of the right triangle."
"For a right triangle, [tex]x^{2}+ y^{2}=z^{2}[/tex], where z is the hypotenuse and x, y are other two sides of the right triangle."
"In a right triangle, csc of angle is the ratio of the hypotenuse to the opposite side of angle."
For given question,
First we find the hypotenuse of the right triangle.
Using Pythagoras theorem,
[tex]\Rightarrow 9^{2} + 12^{2}= r^{2}\\\\ \Rightarrow 81 + 144=r^2\\\\\Rightarrow r=\sqrt{225}\\\\ \Rightarrow r=15[/tex]
so, the hypotenuse is r = 15
Now we find the csc of angle [tex]\theta[/tex]
[tex]\Rightarrow csc(\theta)=\frac{hypotenuse}{opposite~side~of~\theta} \\\\\Rightarrow csc(\theta)=\frac{15}{12}[/tex]
Therefore, the value of [tex]csc(\theta)[/tex] is [tex]\frac{15}{12}[/tex]
Learn more about the csc of angle here:
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