Definitions
Primary Trig Ratios
Sine Law
Cosine Law
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)
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 units
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
A soccer player takes a shot on a standard net that is 7.3 m wide. If the player is 10 m from one goalpost and 14 m from the other, through what angle can a goal be made?
29.9°
400
What type of triangle is required to use the trig functions sine, cosine, and tangent?
Right angle triangles
400
What angle does the rocket need to get launched at to reach the rocket base 300 km above Earth?
θ = 73°
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
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
What are the two possible angles for θ of a triangle with side lengths of 100 units and 75 units with a 40° as marked below:
59° and 121°
500
Scientists in Houston are trying to figure out the distance from a satellite to Cape Canaveral. They know that the satellite is 530 miles from Houston at an 85º angle of elevation, and Houston and Cape Canaveral, in a straight line from one to the other, are 902 miles apart. How far is the satellite from Cape Canaveral?
1005.6 miles