Question

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

A: m∠K = 84°

B: m∠K = 94°

C: k ≈ 3.7 units

D: k ≈ 4.6 units

E: KL ≈ 2.5 units

F: KL ≈ 3.2 units

Answer 1

The correct answers are:

A. m∠K = 84°

C. k ≈ 3.7 units

F. KL ≈ 3.2 units

`|Huntrw6|`

Answer 2

Answer: The correct statements are,

A: m∠K = 84°,

C: k ≈ 3.7 units,

F: KL ≈ 3.2 units

Explanation:

Since, the sum of all three angles of a triangle is 180°,

Therefore,
`m\angle J + m\angle L + m\angle K = 180^(\circ)`

⇒
`58^(\circ) + 38^(\circ) + m\angle K = 180^(\circ)`

⇒
`96^(\circ) + m\angle K = 180^(\circ)`

⇒
`m\angle K = 180^(\circ)-96^(\circ)`

⇒
`m\angle K = 84^(\circ)`

Now, By the sine law,

`(sin38^(\circ))/(2.3) = (sin 84^(\circ))/(k)`

`k =2.3*(sin 84^(\circ))/(sin38^(\circ))`

`k =2.3* 1.61537132861`

`k =3.71535405579\approx 3.7\text{ unit}`

Similarly,

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

`KL =2.3*(sin 58^(\circ))/(sin38^(\circ))`

`KL =2.3* 1.37745844128`

`KL =3.16815441494\approx 3.2\text { unit}\text{ unit}`

⇒ Options A, C and F are correct.