Question

Given the triangle below, which of the following is a correct statement?

A. Sec < B= 3 over 7
B. Cot < B= 3 over 2
C. Sec < B= 7 over 3
D. Cot < C= 1 over 2

I would super appreciate the answer right now! Thanks so much <3

Answer 1

Here, Sec < B= 7/6

Cot < B = 6/3 = 2

Sec < B = 7/6

Cot < C = 3/6 = 1/2

In short, Your Answer would be: Option D

Hope this helps!

Answer 2

Option D is correct

`\cot \angle C = \frac{\text{AC}}{\text{AB}} = (3)/(6) = (1)/(2)`

Explanation:

Using secant and cotangent ratio:'

`\sec \theta = \frac{\text{hypotenuse side}}{\text{Adjacent side}}`

`\cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}}`

In the given triangle:

AB = 6 units , AC = 3 units and BC = 7 units.

Using secant and cotangent ratio:

`\sec \angle B = \frac{\text{BC}}{\text{AB}} = (7)/(6)` ≠
`(3)/(7)`

`\cot \angle B = \frac{\text{AB}}{\text{AC}} = (6)/(3) = 2`≠
`(3)/(2)`

`\sec \angle B = \frac{\text{BC}}{\text{AB}} = (7)/(6)`≠
`(7)/(3)`

`\cot \angle C = \frac{\text{AC}}{\text{AB}} = (3)/(6) = (1)/(2)`

Therefore, the only option which is true is:

`\cot \angle C = \frac{\text{AC}}{\text{AB}} = (3)/(6) = (1)/(2)`