Answer:
First step, find the missing angle (you will need this later on)
We know that the sum of all angles in a triangle equals to 180°, so
180° - 65° - 40° = 75° *that's your angle (next to the point L)
Now, identify each side (as shown in my drawing attached to this message)
The law of sines tells us that
(for example) the side opposite to L (highlighted in pink in the drawing) divided by the sine of the angle at the point L (in our case, 75°) creates a ratio that remains the same for the other sides.
So,
pink side (opposite to L)/ sin 75 (angle at L) = yellow side (opposite to J)/ sin 65 (angle at J) = blue side (opposite to K)/ sin 40 (angle at K)
*Careful, since we were not given the length of one side, you cannot find actual values for each side. Although, you can use the law of sines to logically find out which length is the longest and which one is the shortest.
*Notice that the sine of the angle relates to the length of the coloured sides
Calculate the following: sin 75, sin 40, sin 65.
Once you do that, you will realize that sin 40 = to the smallest value and that sin 75 gives you the largest value.
Thus, sin 40 < sin 65< sin 75
Which corresponds to (from smallest to largest):
blue side, yellow side, pink side
*Now, write your answer in a mathematical format (using J,L,K points)
blue = JL (explanation: it connects the two points, LJ is also a valid answer)
yellow = LK
pink= JK
ANSWER: JL, LK, JK
Explanation:
Use the Law of Sines *because you don't have a right angle triangle.