Question

(will give brainliest!)

Answer 1

Answer:

D) cot(C) = 1/2.

Step-by-step explanation:

We can go through each choice and examine is validity.

Choice A)

We have:

$\displaystyle \sec B=\frac{3}{7}$

Recall that secant is the ratio of the hypotenuse to the adjacent.

With respect to B, the adjacent is 6 and the hypotenuse is 7.

Therefore, sec(B) should be 7/6 instead.

A is incorrect.

Choice B)

We have:

$\displaystyle \cot B=\frac{3}{2}$

Cotangent is the ratio of the adjacent side to the opposite.

With respect to B, the adjacent side is 6 and the opposite side is 3.

Therefore, cot(B) = 6/3 = 2.

B is incorrect.

Choice C)

C is incorrect for the reasons listed in A.

Choice D)

We have:

$\displaystyle \cot C=\frac{1}{2}$

Again, cotangent is the ratio of the adjacent side to the opposite.

With respect to C, the adjacent side is 3 and the opposite side is 6.

So, cot(C) = 3/6 = 1/2.

Therefore, D is the correct choice!