What's the length of KL in inches?

Question

If triangle JKL, sin L=1/3, sin J=3/5, and JK=√5 inches. What's the length of KL in inches?

Answer 1

sin J / KL = sin L / JK  by Law of Sines

(3/5) / KL = (1/3) / √5

1/KL = (5/3)(1/3) / √5

KL = (9/5)√5 which is about 4.025 in.

 

Reasonableness check: angles L & J are 19.47122 deg & 36.8699 deg, respectively, so this is sensible, i.e. the side across from the larger angle is roughly double the smallest angle L.

Answer 2

Draw your triangle and label the triangle appropriately with the side and angle measures as shown.  Then determine whether to use law of sine or law cosine to find the missing side.

Answer 3

The sine of an angle is opposite/hypotenuse of a right triangle with that angle.

 

Triangle JKL is a right triangle -- angle K is 90°.  PLZ draw the triangle.

 

   sin(L) = 1/3 = JK/JL = √5/JL       so JL=3√5

   sin(J) = 3/5 = KL/JL

 

   KL = (KL/JL)JL                   [divide and multiply by JL]

   KL = (3/5)(3√5)

   KL = (9√5)/5

   KL = 4.025 inches   (rounded)