Question

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

Right triangle ABC with AB measuring 6, AC measuring 3, and BC measuring 7.

sec right triangle C equals fraction 3 over 7

cot right triangle B equals fraction 3 over 2

sec right triangle B equals fraction 7 over 3

cot right triangle C equals fraction 1 over 2

http://assets.openstudy.com/updates/attachments/53488782e4b0dfc5ac70e339-shinebrightlikeadimon-1397262745487-openstudy2.gif

Answer 1

Here it is useful to know how each trigonometric function relates the two side measures.
By this I mean, such as the case of sine.
\( \sin \angle A = \dfrac{\text{opposite}}{\text{hypotenuse}} \)
Do you know these relations for cotangent and secant?

Answer 2

is it C or A i'm debating over those two answers @AccessDenied and sorry for taking for ever the wifi disconnected

Answer 3

No worries. What is your reasoning for either one?

Answer 4

I would emphasize again that secant is the reciprocal of cosine:
\( \sec \angle A = \dfrac{\text{hypotenuse}}{\text{adjacent}} \)

Answer 5

So that, in (A), what is \( \sec \angle C \)? For (C), what is \( \sec \angle B\) ? Do they compare with the statement of the answer?

Answer 6

can you paraphrase the last question i didn't understand what you were trying to ask

Answer 7

Well, (A) is saying that \( \sec \angle C = \dfrac{3}{7} \). So instead of trusting the answer, you find \( \sec \angle C \) for yourself using its property: \( \sec \angle C = \dfrac{\text{hypotenuse}}{\text{adjacent}} \). If it is the same as what is given, then the statement is true. I

Answer 8

** If you do not get what is shown, then you have found a wrong answer.

Answer 9

oh i'm so sorry i made a mistake in answer A it was supposed to be B and not C i'm so sorrry

Answer 10

sec right triangle B equals fraction 3 over 7

cot right triangle B equals fraction 3 over 2

sec right triangle B equals fraction 7 over 3

cot right triangle C equals fraction 1 over 2

these are the correct answer choices

Answer 11

Ah. The same check would be done with angle B, though. :)
\( \sec \angle B = \dfrac{3}{7} \) is given. But according to the triangle, the adjacent side to B is 6. The hypotenuse is 7. Thus, \( \sec \angle B = \dfrac{7}{6} \) by definition of secant 7/6 is not 3/7, so (A) cannot be correct. In addition, (C) is also \(\sec \angle B = \dfrac{7}{3} \), but 7/6 is also not 7/3. (C) is false as well.

Get the idea here? We just check the same for each answer choice.

Answer 12

yes that's what everyone has been telling me but in my answer choices i don't have something with 7/6 so i'm so confused and i want to learn how to do this in case i get similar question in the future

Answer 13

In (B) and (D), we need to check cotangent of each angle. Cotangent has the relationship:
\( \cot \angle = \dfrac{\text{adjacent}}{\text{opposite}} \)
So to check (B), we use \(\angle B \) and the sides adjacent and opposite to it. In (D), we check \( \angle C \).

In every case, we just assume the answer choice is not trustworthy and check for ourselves the trig function relationship.

Answer 14

i feel dumb because i still don't know the answer even though your trying more thank your best to help me ~.~

Answer 15

i know adgacent/ opposite is 3/6

Answer 16

would it be D? @AccessDenied

Answer 17

because if you simplify 3/6 you get 1/2?

Answer 18

Yep, (D) looks good to me. :)

Answer 19

thank you

Answer 20

Glad to help!

Answer 21

you did and i'm glad i learn something from you today