Question

ΔJKL has j = 7, k = 11, and m∠J = 18°. Complete the statements to determine all possible measures of angle K. Triangle JKL meets the criteria, which means it is the ambiguous case. Substitute the known values into the law of sines: . Cross multiply: 11sin(18°) = . Solve for the measure of angle K, and use a calculator to determine the value. Round to the nearest degree: m∠K ≈ °. However, because this is the ambiguous case, the measure of angle K could also be °.

Answer 1

we know that
Applying the law of sines

$\frac{k}{sin K} = \frac{j}{sin J} \\ \\ \frac{11}{sin K} = \frac{7}{sin 18} \\ \\ 11*sin 18=7*sin K \\ \\ sin K= \frac{11}{7} *sin 18 \\ \\ sin K=0.4856$

$K=arcsin(0.4856)$
$K=29$°

so
∠J=18°
∠K=29°
∠L=180-(18+29)=133°

the answer Part a) is
the measure of angle K is ≈29°

Part b) the measure of angle K could also be
(180-29)=151°
so
∠J=18°
∠K=151°
∠L=180-(18+151)=11°

the answer Part b) is
the measure of angle K could also be 151°

Answer 2

K = 29°

The triangle is ΔJKL. Therefore,

m∠J = 18°

m ∠ K = ?

j = 7

k = 11

To find m ∠ K we can use sine rule, Therefore,

j / sin 18° = k / sin K

7 / sin 18°  = 11 / sin K

cross multiply

7 sin k  = 11 sin 18°

sin K = 3.39918693812  / 7

sin K = 0.48559813401

K = sin ⁻¹ 0.48559813401

K = 29.0516591712

K ≈ 29°

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