Respuesta :

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.

boffeemadrid

Answer:

ytj

Step-by-step explanation:

In the given triangle JKL, using the Angle sum property, we get

∠J+∠K+∠L=180°

58°+∠K+38°=180°

∠K=84°

Now, using the sine formula, we get

[tex]\frac{k}{sin84^{{\circ}}}= \frac{2.3}{sin38^{{\circ}}}[/tex]

⇒[tex]k=\frac{2.3(sin84^{{\circ}})}{sin38^{{\circ}}}[/tex]

[tex]k=\frac{2.3(0.994)}{0.615}[/tex]

K≈[tex]3.7 units[/tex]

Now,  again using the sine formula, we get

[tex]\frac{KL}{sin58^{{\circ}}}=\frac{3.7}{sin83^{{\circ}}}[/tex]

[tex]KL=\frac{3.7(sin58^{{\circ}})}{sin84^{{\circ}}}[/tex]

[tex]KL=\frac{3.7(0.848)}{0.994}[/tex]

Kl≈[tex]3.2 units[/tex]

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