Question

Which measures are accurate regarding triangle JKL? Check all that apply.

m∠K = 84°

m∠K = 94°

k ≈ 3.7 units

k ≈ 4.6 units

KL ≈ 2.5 units

KL ≈ 3.2 units

Answer 1

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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

`\frac{k}{sin84^{{\circ}}}= \frac{2.3}{sin38^{{\circ}}}`

⇒
`k=\frac{2.3(sin84^{{\circ}})}{sin38^{{\circ}}}`

`k=(2.3(0.994))/(0.615)`

K≈
`3.7 units`

Now, again using the sine formula, we get

`\frac{KL}{sin58^{{\circ}}}=\frac{3.7}{sin83^{{\circ}}}`

`KL=\frac{3.7(sin58^{{\circ}})}{sin84^{{\circ}}}`

`KL=(3.7(0.848))/(0.994)`

Kl≈
`3.2 units`

Answer 2

Option (1), (3) and (6) is correct.

m∠K = 84° , k ≈ 3.7 units and KL ≈ 3.2 units.

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,

`(KL)/(\sin J)=(JL)/(\sin K)=(JK)/(\sin L)`

Substitute the values, we get,

`(KL)/(\sin 58^(\circ))=(k)/(\sin 84^(\circ))=(2.3)/(\sin 38^(\circ))`

Consider the last two ratios, we have,

`(k)/(\sin 84^(\circ))=(2.3)/(\sin 38^(\circ))`

`{k}=(2.3)/(\sin 38^(\circ))* {\sin 84^(\circ)}`

On solving we get,

`{k}=3.71`

Also, now consider the first and last ratio, we get,

`(KL)/(\sin 58^(\circ))=(2.3)/(\sin 38^(\circ))`

`{KL}=(2.3)/(\sin 38^(\circ))* {\sin 58^(\circ)`

`{KL}=3.16`

Thus, k ≈ 3.7 units and KL ≈ 3.2 units.

Option (1), (3) and (6) is correct.