Question

Triangle J K L is shown. The length of L J is 15. Angle K L J is 28 degrees and angle L J K is 110 degrees. Determine the measures of all unknown angles and side lengths of △JKL. Round side lengths to the nearest hundredth. m∠K = ° JK ≈ LK ≈

Answer 1

Answer:

∠JKL = 42°

JK = 10.52

LK = 21.07

Step-by-step explanation:

We will use sine rule to find length of unknown sides.

The sin rule is:

$\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}$

First, lets find the unknown angle ∠JKL.

We know sum of all 3 angles in a triangle is 180, so

28 + 110 + ∠JKL = 180

∠JKL = 180 - 28 - 110 = 42°

Now using sine rule, we find JK:

$\frac{Sin28}{JK}=\frac{Sin42}{15}\\JKSin42=15Sin28\\JK=\frac{15Sin28}{Sin42}\\JK=10.52$

Now using sin rule, we find LK:

$\frac{Sin42}{15}=\frac{Sin110}{LK}\\LKSin42=15Sin110\\LK=\frac{15Sin110}{Sin42}\\LK=21.07$

Answer 2

Answer:

Step-by-step explanation:

Determine the measures of all unknown angles and side lengths of △JKL. Round side lengths to the nearest hundredth.

m∠K = 42°  

JK ≈  10.52

LK ≈ 21.07