Answer:
x = 67° (nearest whole degree)
Step-by-step explanation:
Sine Rule
[tex]\sf \dfrac{sin(A)}{a}= \dfrac{sin(B)}{b}= \dfrac{sin(C)}{c}[/tex]
where A, B and C are the angles, and a, b and c are the sides opposite the angles
Given information
From inspection of the triangle:
- A = 38°
- a = 12
- B = x°
- b = 18
Finding x:
Substitute given values into the formula and solve for x:
[tex]\sf \implies \dfrac{sin(38)}{12}= \dfrac{sin(x)}{18}[/tex]
[tex]\sf \implies 18\cdot\dfrac{sin(38)}{12}= sin(x)[/tex]
[tex]\sf \implies sin(x)=\dfrac32sin(38)[/tex]
[tex]\sf \implies x=sin^{-1}\left(\dfrac32sin(38)\right)[/tex]
[tex]\sf \implies x=67.44208077...[/tex]
Final Solution
x = 67° (nearest whole degree)
