Answer: The correct statements are,
A: m∠K = 84°,
C: k ≈ 3.7 units,
F: KL ≈ 3.2 units
Step-by-step explanation:
Since, the sum of all three angles of a triangle is 180°,
Therefore, [tex]m\angle J + m\angle L + m\angle K = 180^{\circ}[/tex]
⇒ [tex]58^{\circ} + 38^{\circ} + m\angle K = 180^{\circ}[/tex]
⇒ [tex]96^{\circ} + m\angle K = 180^{\circ}[/tex]
⇒ [tex] m\angle K = 180^{\circ}-96^{\circ}[/tex]
⇒ [tex] m\angle K = 84^{\circ}[/tex]
Now, By the sine law,
[tex]\frac{sin38^{\circ}}{2.3} = \frac{sin 84^{\circ}}{k}[/tex]
[tex]k =2.3\times\frac{sin 84^{\circ}}{sin38^{\circ}}[/tex]
[tex]k =2.3\times 1.61537132861[/tex]
[tex]k =3.71535405579\approx 3.7\text{ unit}[/tex]
Similarly,
[tex]\frac{sin 38^{\circ}}{2.3} = \frac{sin 58^{\circ}}{KL}[/tex]
[tex]KL =2.3\times\frac{sin 58^{\circ}}{sin38^{\circ}}[/tex]
[tex]KL =2.3\times 1.37745844128[/tex]
[tex]KL =3.16815441494\approx 3.2\text { unit}\text{ unit}[/tex]
⇒ Options A, C and F are correct.
