Given:
GE = f = 4.3
GF = e = x
m∠G = 64° and m∠E = 85°
To find:
The value of x.
Solution:
Triangle sum theorem:
Sum of the adjacent angles in a triangle = 180°
m∠E + m∠F + m∠G = 180°
64° + m∠F + 85° = 180°
149° + m∠F = 180°
Subtract 149° from both sides, we get
m∠F = 31°
Using sine formula:
[tex]$\frac{e}{\sin E} =\frac{f}{\sin F}[/tex]
[tex]$\frac{x }{\sin 85^\circ} =\frac{4.3}{\sin 64^\circ}[/tex]
[tex]$\frac{x }{0.99} =\frac{4.3}{0.9}[/tex]
Multiply by 0.99 on both sides.
[tex]$\frac{x }{0.99}\times 0.99 =\frac{4.3}{0.9} \times 0.99[/tex]
[tex]x = 4.73[/tex]
[tex]x = 4.7[/tex] (nearest tenth)
The value of x is 4.7 units.
