Question

Find the value of tan θ for the angle shown. (2 points)

Answer 1

Answer:

The correct answer is:

                               Option: b

b) tan θ = negative four times square root of thirty-three divided by thirty-three

Step-by-step explanation:

We know that the tangent trignometric ratio of an angle is the ratio of the opposite side to the adjacent side corresponding to the given angle.

i.e. from the figure we have:

$\tan (360-\theta)=\dfrac{4}{\sqrt{33}}\\\\i.e.\\\\-\tan \theta=\dfrac{4}{\sqrt{33}}\\\\i.e.\\\\\tan \theta=-\dfrac{4}{\sqrt{33}}$

on rationalizing the denominator we have:

$\tan \theta=-\dfrac{4}{\sqrt{33}}\times \dfrac{\sqrt{33}}{\sqrt{33}}\\\\i.e.\\\\\tan \theta=-\dfrac{4\sqrt{33}}{33}$

Answer 2

square root (33) = 5.7445626465

arc tan (5.7445626465 / -4) =

arc tan (-1.4361406616) = -55.15

360 -55.15 = 304.85 degrees