"The Right Kind of Trig"
"Law of Sines and Sorcery"
"Circle It!"
"Spells from the past!"
100
A picture frame is in the shape of a 30-60-90 triangle. What's the length of the hypotenuse if the shorter leg is 7 inches long?
14 inches.
100
What law is best used when you know two angles and one side (ASA or AAS situations)?
The Law of Sines.
100
What is the measure of an arc that is exactly half the circle?
180 degrees.
100
Type of angles shown...
Vertical angles
200
In a 45-45-90 triangle, if the hypotenuse is 12 inches, how long is each leg?
6\sqrt{2} inches.
200
What is the formula for the Law of Sines?
\frac{\sin(A)}{a} + \frac{\sin(B)}{b} + \frac{\sin(C)}{c}
200
The radius of the Hogwarts clock tower is 10 meters. What's the length of a 90-degree arc?
5\pi meters.
200
Name the angles shown...
Corresponding angles
300
Harout is flying on his magic flying Alhambra guitar. His path makes an angle of 35° with the ground. If he knows how far he has flown along the path at any time, which trigonometric ratio should he use to find his height above the ground?
Sine (since sine = opposite / hypotenuse, and his path is the hypotenuse).
300
Jacob tries to find an unknown angle of a triangle using all three sides only. What magical law does he use?
He uses the Law of Cosines like a boss.
300
What's the difference between arc measure and arc length?
Arc measure is in degrees, while arc length is the distance along the circle.
300
A transformation that does not change the size of shape of a figure.
Rigid transformation
400
Michelle is flying from Simi Valley to Santa Monica in her new helicopter.
Her initial path makes an angle of elevation of 28° with the ground. After flying 500 meters along this path, how far is Michelle horizontally from her starting point?
Use cosine, since cos(28°) = adjacent / 500 → adjacent = 500 × cos(28°) ≈ 500 × 0.8829 ≈ 441.45 meters.
400
Elisa and Savannah are planning a magical quest to slay the dragon that ate Makayla. Just swallowed the poor thing up. It was bad.
They need to travel from their castle to the enchanted forest, which lies 8 miles east. From there, she must reach the dragon’s lair, which is 12 miles away, but the path between the enchanted forest and the dragon’s lair forms a 110° angle with her original path from the castle.
What is the direct distance from their castle to the dragon’s lair?
Approximately 16.54 miles from the dragon’s lair.
400
At the enchanted Quidditch stadium, the audience seating is arranged in a giant circular arc. The stadium has a radius of 150 meters. The seating area stretches along an arc that measures 135 degrees.
Find the length of the seating area along the arc, and determine what fraction of the entire stadium's circle the seating area covers.
Arc Length: \approx 353.43 meters.
Fraction of the circle: \frac{3}{8} .
400
Which transformation is not a rigid motion?
Dilation