Question

Given the triangle and equation below, what is the value of x?
csc∠A + tan∠C = 5x

fraction 35 plus 5 times the square root of 13 over 6

fraction 7 plus square root of 13 over 30

fraction 7 plus 6 times the square root of 13 over 210

fraction 35 plus 30 times the square root of 13 over 42

Answer 1

is x suppose to be the legnth of the side on the left?

Answer 2

That is part of the reason why I am confused. See, I don't know what x is. I am starting to believe that you have to solve the equation on the bottom in order to get x. However, I am unsure as to how to solve that as well.

Answer 3

Let
A=6
B=?
C=7

substitute into the equation:
\[A^2 + B^2 = C^2\]

solve for B, B will be the value for x, which is the missing side length.

Answer 4

Yes, B = 3.60.
That is how far I got before doing some jibber jabber with csc and tan

Answer 5

then ur done! that is all you can do, unless they want you to find the angles ..

Answer 6

wait.. not so..

Answer 7

Oh. ok. Thanks for your help. :)

Answer 8

Oh, what's missing?

Answer 9

csc∠A + tan∠C = 5x
1/sinA + tanC = 5x

so we need to find the angle of A....
wait.. how do we know which anlge on the drawing is A?

Answer 10

The best I can figure is that A is the angle on the top, is that what you think too?

Answer 11

if so, use the law of sines.
do sin90/7 = sinA/6 and solve for A

Answer 12

I did not realize how poorly the choices came out, this should help

Answer 13

then we need to solve for C, so do
sinC/3.6 = sin90/7
solve for C

Answer 14

Yeah, I agree with A being angle on top

Answer 15

we can solve this i think.

just do what I said, solve for A and for C using the law of sines

Answer 16

Sorry, I was having a brainfart. Just to make sure I am back on track, A =58 correct?

Answer 17

If so, then C = 32

Answer 18

I really can't say, i don't have a calc with trig near me!

Answer 19

1/sinA + tanC = 5x
1/sin(58) + tan(32) = 5x
solve for x

Answer 20

Okay, I did SOH
6/7
0.857 sin-1
I got 58
then for C, I took 180-90-58=32

Answer 21

oh, smart move for finding C

Answer 22

Thanks :)

Answer 23

I got an answer for x using your method(thanks by the way) however, the answer choices for the question are in the how to solve for it, so naturally, I looked for what we did as a choice, but no luck.

Answer 24

what did you get for the value of x?

Answer 25

have you gone through each choice and converted it to a decimal number and then check it witht he value of X you solved for?

Answer 26

I got 1.796 for x

Answer 27

Ugh, I thought the answer choices were asking for how to solve it, my bad. I will check now

Answer 28

^_^

Answer 29

Use the figure and calculate angle C. It is a right triangle and Cos C=6/7 thus angle C is 31 degrees (inverse cos function) The remaining angle is 90-31 or 59 degrees. That would be angle A.

Answer 30

I believe it is A because the answer to A is only a few points off, so it could be from rounding.

Answer 31

Another reason for my answer possibly being off could be in the angles, because radar, you got 1 off from mine. I am sure mine are wrong, so I am going to go with answer choice A unless if one of you disagree.

Answer 32

Now use a calculator and calculate Csc 59 degrees. Csc 59= 1/sin 59 = 1.1666
Now calculate Tan 31 degrees which is 0.600.
The equation provided in the problem substituting values obtained:
1.16666 + .600 = 5x
1.7675 = 5x
x=0.3535
Seems like a strange answer, possibly I strayed from the correct path.

Answer 33

No, you are right! I accidentally made a mistake and thought my answer as being x, multiplying it by 5... Which makes B correct, as it is spot on. Thanks :)

Answer 34

And demolisionwolf, thanks for helping me out a lot also, as for you to radar, you guys have a good night.