Answer:
The value of tan θ is:
[tex]\tan \theta=-\dfrac{4}{\sqrt{33}}[/tex]
Step-by-step explanation:
From the given right angled triangle we have:
Base of the triangle i.e. OA is: √33 units
and Perpendicular length of triangle i.e. AB is: 4 units
Hence, in the given right angled triangle we will use the trignometric ratio corresponding to the angle (360°-θ) as:
[tex]\tan (360-\theta)=\dfrac{perpendicular}{base}\\\\\\\tan (360-\theta)=\dfrac{4}{\sqrt{33}}[/tex]
As we know that:
[tex]\tan (360-\theta)=-\tan \theta[/tex]
Hence,
[tex]-\tan \theta=\dfrac{4}{\sqrt{33}}\\\\\\i.e.\\\\\\\tan \theta=-\dfrac{4}{\sqrt{33}}[/tex]
Hence, the answer is:
[tex]\tan \theta=-\dfrac{4}{\sqrt{33}}[/tex]
