Answer:
Option D is correct
[tex]\cot \angle C = \frac{\text{AC}}{\text{AB}} = \frac{3}{6} = \frac{1}{2}[/tex]
Step-by-step explanation:
Using secant and cotangent ratio:'
[tex]\sec \theta = \frac{\text{hypotenuse side}}{\text{Adjacent side}}[/tex]
[tex]\cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}}[/tex]
In the given triangle:
AB = 6 units , AC = 3 units and BC = 7 units.
Using secant and cotangent ratio:
[tex]\sec \angle B = \frac{\text{BC}}{\text{AB}} = \frac{7}{6}[/tex] ≠ [tex] \frac{3}{7}[/tex]
[tex]\cot \angle B = \frac{\text{AB}}{\text{AC}} = \frac{6}{3} = 2[/tex]≠ [tex]\frac{3}{2}[/tex]
[tex]\sec \angle B = \frac{\text{BC}}{\text{AB}} = \frac{7}{6}[/tex]≠ [tex]\frac{7}{3}[/tex]
[tex]\cot \angle C = \frac{\text{AC}}{\text{AB}} = \frac{3}{6} = \frac{1}{2}[/tex]
Therefore, the only option which is true is:
[tex]\cot \angle C = \frac{\text{AC}}{\text{AB}} = \frac{3}{6} = \frac{1}{2}[/tex]
