An example of SOH with Christian Ozera
Christian Ozera is getting sent to detention for defending his friends, but maybe not in the smartest way. Instead of speaking up, he used fire magic to burn a note from the professors hand. Christian was sitting up above in a balcony listening to the lecture from his professor down on ground level. To plan his escape after he burns the note, Christian needs to know the angle of depression from himself down to his professor in order to plan his escape. He knows the distance between himself and the professor is 45 feet from the balcony to the professor on the ground level, and the distance between the professor and the ground level door is 20 feet. Christian is on the balcony right above the door. What is the angle of depression Christian needs to know in order to plan his escape?
Opposite = 20 Feet
Hypotenuse = 45 Feet
SOH = Sin^-1(20/40)
Sin^-1(20/40) = 30
Angle ? = 30°
Hypotenuse = 45 Feet
SOH = Sin^-1(20/40)
Sin^-1(20/40) = 30
Angle ? = 30°
Now Rose and Dimitri are going to show an example of CAH
Dimitri and Rose are practicing throwing knives into a tree. Rose throws a knife near the top of a tree trunk. At the angle Rose threw the knife, the handle tilts downwards toward Dimitri and herself. Curious, Rose wants to know the angle the knife makes with the tree. She and Dimitri calculate that the distance from themselves to the knife is 21 feet and the tree is only 12 feet tall. Using CAH, calculate the angle the knife makes with the tree.
Adjacent = 12 Feet
Hypotenuse = 20 Feet
CAH = Cos^-1(Adjacent/Hypotenuse)
Cos^-1(Adjacent/Hypotenuse) = Cos^-1(12/20)
Angle ? = 53°
Hypotenuse = 20 Feet
CAH = Cos^-1(Adjacent/Hypotenuse)
Cos^-1(Adjacent/Hypotenuse) = Cos^-1(12/20)
Angle ? = 53°
Let't talk about TOA with Mason
Mason and the other guardians are playing a game of capture the flag to practice their observation skills. Mason is designated to hide the flag for his group. He climbs up onto a roof and ties it at the top, hoping to obscure it from sight. He climbs back down from the hiding spot and walks a little ways off. To make sure nobody can see the flag, Mason wants to calculate the angle the flag, which is angled toward him, makes with the post it is tied to on the edge of the roof. Mason stands 225 feet away from the building and the flag rest 190 feet straight up from the ground. What is the angle the flag makes with its post?
Adjacent = 190 Feet
Opposite = 225 Feet
TOA = Tan^-1(Opposite/Adjacent)
Tan^-1(Opposite/Adjacent) = Tan^-1(190/225)
Angle ? = 40°
Opposite = 225 Feet
TOA = Tan^-1(Opposite/Adjacent)
Tan^-1(Opposite/Adjacent) = Tan^-1(190/225)
Angle ? = 40°