Answer:
Option (1), (3) and (6) is correct.
m∠K = 84° , k ≈ 3.7 units and KL ≈ 3.2 units.
Step-by-step explanation:
Given : ∠J = 58° , ∠L = 38° and length of side JK = 2.3 units.
We need to check all the options and choose that follows.
First we find the measure of ∠K
Using angle sum property , Sum of angles of a triangle is 180°
⇒ ∠J + ∠k + ∠L = 180°
⇒ 58° + ∠k + 38° = 180°
⇒ ∠k + 96° = 180°
⇒ ∠k = 180° - 96°
⇒ ∠k = 84°
Also using sine rule on ΔJKL , we get,
[tex]\frac{KL}{\sin J}=\frac{JL}{\sin K}=\frac{JK}{\sin L}[/tex]
Substitute the values, we get,
[tex]\frac{KL}{\sin 58^{\circ}}=\frac{k}{\sin 84^{\circ}}=\frac{2.3}{\sin 38^{\circ}}[/tex]
Consider the last two ratios, we have,
[tex]\frac{k}{\sin 84^{\circ}}=\frac{2.3}{\sin 38^{\circ}}[/tex]
[tex]{k}=\frac{2.3}{\sin 38^{\circ}}\times {\sin 84^{\circ}}[/tex]
On solving we get,
[tex]{k}=3.71[/tex]
Also, now consider the first and last ratio, we get,
[tex]\frac{KL}{\sin 58^{\circ}}=\frac{2.3}{\sin 38^{\circ}}[/tex]
[tex]{KL}=\frac{2.3}{\sin 38^{\circ}}\times {\sin 58^{\circ}[/tex]
[tex]{KL}=3.16[/tex]
Thus, k ≈ 3.7 units and KL ≈ 3.2 units.
Option (1), (3) and (6) is correct.
