Respuesta :

3/4 root 10
you make a right triangle. use Pythagorean theorem. and find the opposite side. then reduce the radical of 160. and do tan and then flip them around to make cot.

Answer:

The value of:

          [tex]\cot \theta=\dfrac{3}{4\sqrt{10}}[/tex]

Step-by-step explanation:

We are given,

[tex]\cos \theta=\dfrac{3}{13}[/tex]

We know that cos θ is the ratio of base and hypotenuse of a right angled triangle corresponding to θ.

On applying Pythagorean Theorem in ΔABC we get:

[tex]13^2=3^2+a^2\\\\\\i.e.\\\\\\169=9+a^2\\\\\\a^2=160\\\\\\i.e.\\\\\\a=4\sqrt{10}[/tex]

Hence, the value of [tex]\cot \theta[/tex] is defined as the ratio of base to perpendicular length of the triangle.

              Hence,

         [tex]\cot \theta=\dfrac{3}{4\sqrt{10}}[/tex]