Question

Find L to the nearest degree. J,K,L,4cm,10.78cm.

Answer 1

To find angle L to the nearest degree, we can use the law of cosines.

Let's call the angle opposite side J "j" and the angle opposite side K "k". The law of cosines states:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the side opposite angle C, a and b are the other two sides, and C is the angle opposite side c.

In our case, L is the angle opposite side J and K, so we can rewrite the formula as:

j^2 = 4^2 + 10.78^2 - 2*4*10.78*cos(L)

Solving for cos(L), we get:

cos(L) = (16 + 116.368 - j^2)/(2*4*10.78)
cos(L) = (132.368 - j^2)/(86.24)

Since we wanted L to the nearest degree, we can use inverse cosine (arccos) to find L:

L = arccos((132.368 - j^2)/(86.24))

We don't have the angle j, but we can solve for j using the law of sines which states:

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

Using this, we can find j:

sin(L)/10.78 = sin(K)/4

We can simplify this to:

sin(L) = 10.78*sin(K)/4

Now, we can substitute this into our formula for cos(L) and solve for L.