Definitions
Primary Trig Ratios
Sine Law
Cosine Law
Mystery
100
This trigonometry ratio relates the hypotenuse and adjacent side
Cosine
100
What is the value of sin(30o)?
1/2 or 0.5
100
When is it appropriate to use Sine Law?
A. Two angles and one side (AAS) or (ASA)
B. Two sides and a non-included angle (SSA)
100
When is it appropriate to use the Cosine Law?
A. All 3 sides (SSS)
B. Two sides and the included angle(SAS)
100
If angle D is 131°, side length d is 25 units, and side length e is 8 units, how many triangles can be formed?
1 triangle
200
The diagram below represents the angle of ________.
Elevation
200
Given the diagram, what is the value of x?
x = 8.8 units
200
If ∠B = 14°, ∠C = 45°, and b = 5.2 units, find c using the Law of Sines.
15.2 units
200
If a = 21.5 units, b = 13 units, and ∠C = 39°, find c using the Law of Cosines
14.0 units
200
If angle C is 61°, side length a is 35 units, and side length c is 32 units, how many triangles can be made?
2 triangles
300
In right angled triangles, the side across from the right angle is referred to as the ______________.
Hypotenuse
300
Given the following diagram, what is the value of x?
x = 6.9 m
300
If a = 12 units, ∠B = 27°, and b = 15 units, find ∠A using the Law of Sines.
21°
300
Lionel Messi takes a shot on a standard net that is 7.3 m wide. If Messi is 10 m from one goalpost and 14 m from the other, through what angle can a goal be made?
30°
300
The Savioa S.21 seaplane is flying at an altitude of 11,000 ft. Porco Rosso wants to make a smooth descent to the water at an angle of depression of 5°. How far from the water should Porco Rosso begin his descent?
125,731 ft
400
What type of triangle is required to use the trig functions sine, cosine, and tangent?
Right angle triangles
400
In Haikyuu!!, Ushijima is known for his powerful spike. He has a jumping reach of 3.45 meters. When he spikes the volleyball, the ball's trajectory forms a 60° angle with the vertical line of his jump. How far horizontally will the ball travel before hitting the floor, assuming the ball follows a straight line after leaving Ushijima's hand?
6.0 meters
400
By what factor is side b larger than side a in the triangle below?
b = 1.51a
400
Suppose a boat leaves port, travels 10 miles, turns 20 degrees, and travels another 8 miles. How far from port is the boat?
17.7 miles
400
When the Straw Hat Pirates are trying to get to the Grand Line, they eventually reach the Twin Cape Lighthouse which is built on top of a 25 ft tall cliff. The angle of elevation from the Strawhat's ship, the Going Merry, to the top of the lighthouse, which is 35 ft tall, is 25°. How far is the Going Merry from the cliff?
128 ft
500
When solving for the missing angle θ, what functions must you use? Hint: think of what you put into the calculator
The inverse trig functions (sin-1, cos-1, tan-1)
500
Simon bought a new shop and wants to order a new sign for the roof of the building. From point P, he finds the angle of elevation of the roof, from ground level, to be 31º and the angle of elevation of the top of the sign to be 42º. If point P is 24 feet from the building, how tall is the sign to the nearest tenth of a foot?
7.2 ft
500
Miwa’s "New Shadow Style" cursed technique creates a circular domain with a radius of 2.2 meters around her. At a certain moment, Geto is 2.75 meters away from Miwa, walking due East. His walking path makes an angle of 47° with the line connecting Miwa and his current position. If Geto continues walking along this straight path, what distance will he travel while staying within Miwa’s domain?
1.8 m
500
The Rebel Alliance is trying to determine the distance between the Millennium Falcon and planet Tattoine. They know that the Falcon is 530 light-years away from the planet Coruscant, at an 85º angle of elevation from their Rebel Headquarters on Coruscant's surface. Additionally, the distance between Coruscant and Tatooine in a straight line is 902 light-years. How far is the Millennium Falcon from Tatooine?
1005.6 light-years away
500
When flying in a plane over Prince Edward Island it is possible to see all the way across the island from one side to the other. The pilot of a small plane spots the western edge of the island at an angle of depression of 61° and the eastern edge of the island with an angle of depression of 3°. If the plane is flying at an altitude of 10.5 km, how long is Prince Edward Island?
206.2 km