For ΔGHJ, m∠J = 39°, h = 36 in., and j = 42 in. Find m∠H to the nearest tenth of a degree.

Answer 1

Try using the Law of Sines.

sin(J)/j = sin(H)/h

Answer 2

Hey Meggie!

Your problem can be solved using the Law of Sines which states the following:

a/Sin(A) = b/Sin(B) = c/Sin(C)

where the lower case letters are the triangle sides and the upper case letters are the angles across from their corresponding sides (so a is the side across from angle A).

We can set up a similar equation with h and j:

j/Sin(J) = h/Sin(H)

Now sub in the numbers you already know and solve for missing angle H:

42/Sin(39) = 36/Sin(H)

Sin(H) X (42/Sin (39)) = 36

Sin(H) = 36 ÷ (42/Sin(39))

H = Sin^-1(36 ÷ (42/Sin(39)))

H= 32.6439.....

H= 32.6° (Rounded to the nearest tenth of a degree)

If you are following along with your calculator make sure it is in degree mode (not radian), and make sure you are following the order of operations.

Hope this helps!