Question

I do not understand this Geometry question. Can some one help?

question:Given the triangle and equation below, what is the value of x?

Right triangle ABC with AC measuring 7 and BC measuring 6.

sec∠C - cot∠A = 3x

Answer 1

Here is the picture and possible answers:

Answer 2

Do you know how to find the secant of angle C?

Answer 3

I think so:

Secant of c = 7/6
This is what I did for this part:

1/cosine(x) = 7/6
6 = 7(cosine(x))
.857 = cosine(x)
31.01 = x

Answer 4

well there's no need to find the angle since we really don't care about the angle itself

Answer 5

also, it's better leave it as a fraction

Answer 6

so sec(C) = 7/6

Answer 7

oh ok

Answer 8

what about the cotangent of angle A?

Answer 9

well cotangent = adjacent/opposite but I only have the hypotenuse and the opposite

Answer 10

do you know how to find the adjacent side?

Answer 11

Remember that with any right triangle with legs A and B (and hypotenuse C), we know that


A^2 + B^2 = C^2

Answer 12

ya I just thought of that when you posted the question:)

Answer 13

alright great :)

Answer 14

so the adjacent side = 3.6

Answer 15

keep everything as exact as you can

Answer 16

so keep the square roots

Answer 17

\[\sqrt{13}\]

Answer 18

so what did you get before you got 3.6?

Answer 19

good

Answer 20

so what is cot(A) then?

Answer 21

so cotangent = \[\sqrt{13}\]/6

Answer 22

over 6

Answer 23

good

Answer 24

so

sec∠C - cot∠A = 3x

becomes

7/6 - sqrt(13)/6 = 3x

Answer 25

so just simplify from there

Answer 26

yes and divide both sides by 3 afterwards to solve for x

Answer 27

ok so x = 7 - \[\sqrt{13}\] over 18

Answer 28

That is one of my choices
thanks a lot your a great teacher!

Answer 29

yes I'm assuming you mean \[\Large x = \frac{7-\sqrt{13}}{18}\]

Answer 30

yup

Answer 31

thanks, I'm glad I could help you out