Answer:
VJ ≈ 6.7 in
Step-by-step explanation:
Using the Sine rule in Δ XYJ
∠ X = 180° - (105 + 35)° = 180° - 140° = 40°, thus
[tex]\frac{XJ}{sinV}[/tex] = [tex]\frac{VJ}{sinX}[/tex], that is
[tex]\frac{6}{sin35}[/tex] = [tex]\frac{VJ}{sin40}[/tex] ( cross- multiply )
VJ sin35° = 6 sin40° ( divide both sides by sin35° )
VJ = [tex]\frac{6sin40}{sin35}[/tex] ≈ 6.7 ( to the nearest tenth )
Answer: VJ = 6.7 inches
Step-by-step explanation:
Considering the given triangle JVX, to determine VJ, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
VJ/SinX = VX/SinJ = JX/SinV
The sum of the angles in a triangle is 180°. It means that
X = 180 - (105 + 35) = 40°
Therefore
VJ/Sin 40 = 6/Sin 35
Cross multiplying, it becomes
VJSin35 = 6Sin40
0.5736VJ = 6 × 0.6428
0.5736VJ = 3.8568
VJ = = 3.8568/0.5736
VJ = 6.7 inches
