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

csc∠A + tan∠C = 5x

Question

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

anonymous · Answer

wheres the triangle?

anonymous · Answer

attachment

anonymous · Answer

do you know the answer ?

anonymous · Answer

right you can find the length of side AB by pythagoras
ab = sqrt(7^2 - 6^2) = sqrt13

csc A = AC/AB = 7 / sqrt13
tan C =  AB / BC = sqrt13 / 6

so to find x you solve :

7/sqrt13 + sqrt13 / 6  = 5x

anonymous · Answer

can you complete this?

anonymous · Answer

so is it 7+sqrt13 / 30?

anonymous · Answer

lets see
we can multiply through by the LCM 6 sqrt13:
42 +  13 = 30sqrt13x
x = 55 /  30sqrt13 = 11 / 6sqrt13

anonymous · Answer

- which is 0.508 to 3 dec places

anonymous · Answer

do you follow my solution mis.kayla?

anonymous · Answer

we can solve a fractional equation by multiplying every term by the LCM:

3              2
-     +     --   =       8
5x            3

LCM = 15x


3 * 15x         2 * 15x
------    +    ------    =   15x*8
   5x                  3

simplifying:

3*3  +  2 * 5x  =  120x