Castiel finds out how to find a missing angle with Law of Sines
Castiel has to draw an angel trap on a nearby tree that's leaning to the side. Castiel decides he can't hold his angel blade and draw the trap at the same time, so he sticks his angel blade in the ground. He notices the blade points to the tree at an angle and decides that finding the angle could help him determines where to draw the trap. He knows the tree is 100 feet tall, and the angle the tree makes with the ground is 50 degrees. He also quickly discovers that the diagonal from the ground to the top of the tree is 150 feet. Based on these three measurements and the law of sines, what is the angle the blade makes with the ground?
Meg works with Law of Sines with missing sidelengths
Meg wants to test to see how far she can throw an angel blade. She stands at the bottom of a steep 75 foot slope and wants to see if the angel blade will reach the top when thrown. When she extends the blade, it creates a 52 degree angle with the ground. Meg sees that the slop goes back down even steeper on the other side, making a 73 degree angle with the ground. Using Megs calculations and the law of sines, calculate the length of the opposite side of the slope.