Answer:
x ≈ 49.7°
Step-by-step explanation:
Since, the given triangle is an isosceles triangle,
Two sides having measure 17 units are equal.
Opposite angles of these equal sides will be equal.
Measure of the third angle = 180° - (x + x)°
By sine rule,
[tex]\frac{\text{sinx}}{17}=\frac{\text{sin}(180-2x)}{22}[/tex]
[tex]\frac{\text{sinx}}{17}=\frac{\text{sin}(2x)}{22}[/tex] [Since, sin(180 - θ) = sinθ]
[tex]\frac{\text{sinx}}{17}=\frac{2(\text{sin}x)(\text{cos}x)}{22}[/tex]
[tex]\frac{\text{sinx}}{17}=\frac{(\text{sin}x)(\text{cos}x)}{11}[/tex]
[tex]\frac{1}{17}=\frac{(\text{cos}x)}{11}[/tex]
cos(x) = [tex]\frac{11}{17}[/tex]
x = 49.68°
x ≈ 49.7°
