+0

0
168
3
+4

Jan 22, 2020

#1
+25532
+3

Please find the value of x.

sin-rule:

$$\begin{array}{|rcll|} \hline \dfrac{\sin(\theta)}{24} &=& \dfrac{\sin(A)}{3x-3} \\\\ \mathbf{\dfrac{\sin(A)}{\sin(\theta)}} &=& \mathbf{\dfrac{3x-3}{24}} \\ \hline \end{array}$$

sin-rule:

$$\begin{array}{|rcll|} \hline \dfrac{\sin(\theta)}{44} &=& \dfrac{\sin(180^\circ-A)}{5x} \quad | \quad \sin(180^\circ-A) =\sin(A) \\\\ \dfrac{\sin(\theta)}{44} &=& \dfrac{\sin(A)}{5x} \\\\ \mathbf{\dfrac{\sin(A)}{\sin(\theta)}} &=& \mathbf{\dfrac{5x}{44}} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \dfrac{\sin(A)}{\sin(\theta)} = \dfrac{3x-3}{24} &=& \dfrac{5x}{44} \\\\ \dfrac{3x-3}{24} &=& \dfrac{5x}{44} \\\\ 44(3x-3) &=& 24*5x \\ 132x- 132 &=& 120x \quad | \quad +132 \\ 132x &=& 120x +132 \quad | \quad -120x \\ 132x-120x &=& 132 \\ 12x &=& 132 \quad | \quad : 12 \\ x &=& 132 \quad | \quad : 12 \\ \mathbf{x} &=& \mathbf{11} \\ \hline \end{array}$$

Jan 22, 2020
edited by heureka  Jan 23, 2020
#2
+1

Hi Heureka,

I've one question why is $$sin(\theta )=sin(180-A)$$

Guest Jan 22, 2020
#3
+25532
+2

Hi Guest,

here is set   $$\mathbf{\sin(180^\circ-A) =\sin(A)}$$

heureka  Jan 23, 2020
edited by heureka  Jan 23, 2020