Question

Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

What is the approximate measure of angle K? Use the law of sines to find the answer.

20°
34°
41°
53°

Answer 1

B) 34

Explanation:

Answer 2

The approximate measure of angle K is 34°

Explanation:

In ΔJKL

∠L = 105°

JK = 4.7

JL = 2.7

Sine Rule:

`(SinA)/(a) = (SinB)/(b)= (SinC)/(c)`

So,
`(SinL)/(JK) = (SinK)/(JL)\\(SinL)/(4.7) = (SinK)/(2.7)\\(Sin 105)/(4.7) = (SinK)/(2.7)\\(Sin 105 * 2.7)/(4.7) = SinK\\((0.9659 * 2.7))/(4.7) = Sin K\\(2.60793)/(4.7) = Sin K\\0.5549 = Sin K\\Sin^(-1)(0.5549)= K\\K = 33.70`

K ≈ 34°

So, Option B is true

Hence The approximate measure of angle K is 34°