Define the ratios for sine, cosine and tangent in terms of Opposite, Adjacent and Hypotenuse
sinθ =O/H
cosθ =A/H
tanθ =O/A
State the sine rule
Sine law: A/SinA = B/SinB = C/SinC
State the cosine rule
a^2 = b^2 + c^2 -2bc(CosA)
If b=3 and h=4, A=?
What is A=6
Define tangent in terms of other trigonometric functions
Tanθ = sinθ /cosθ
In △ABC, where ∠A = 40˚, a = 22mm, and b = 27mm.
Find both possible values of ∠ABC
Case 1 ∠B1 = 52˚ ∠C = 88˚ c = 34.2mm Case 2 ∠B1 = 128˚ ∠C = 12˚ c = 7.1mm
Determine side a in △ABC to one decimal, if ∠B = 130˚, b = 50mm, and c=20mm.
a = 34.8mm
Write the formula for the area of a triangle in terms of A, b and c
Area = 1/2*b*c*sinA
Explain how both sine and cosine functions are represented on the unit circle
sinθ = y axis value,
cosθ = x-axis value
△ABC with ∠A = 44˚, ∠B = 56˚, and b=17m. Find the remaining unknowns
∠C = 80˚ c = 20.2m a = 14.2m
In triangle ABC, C=37º, a=8 and b=11.Find the length of side c
c=6.7
For a triangle with angle A = 40 Degrees, and sides b = 12cm and c = 14cm, find the Area
54cm^2
Determine all unknown side lengths and angles. Round each side length to the nearest unit and each angle to the nearest degree.
Angle C: 90°, c: 70 cm , b: 30 cm. Find a, A, B.
a = 63cm A = 65˚ B = 25˚
In what two situations can the cosine rule be used
- two sides and an included angle are given
- three sides are given
In △EFG, if ∠F = 18˚, f = 15.3m and g = 21.3m, determine the number of possible triangles that could be drawn.
f/(sinF) = g/(sinG)
sinG = g(sinF)/f = 21.3(sin18˚)/15.3
G = sin^-1(.4302) = 25.48 Degrees, or 154.52 degrees
∴2 possible triangles
Three fast food restaurants are located in Cranbourne forming a triangle on the map. The distance from Pizza Hut to McDonald's to Burger King back to Pizza Hut is 3.5km, 9.2km, and 7.8km, respectively. Find the angle between the route joining McDonald’s And Burger King and the route joining McDonald’s and Pizza Hut.
Using the Cosine law, ∠M = 55.96˚
Write a derivation of the formula:
Area = 1/2*b*c*sinA
See derivation on the board
Kobe, Carter, Emory, Jackson, Josh, and Cameron are all out playing golf. Carter smashes a drive with an angle of elevation of 15 degrees. If the highest point of the drive was at 60 meters, how far was the ball when it was at 60 meters in the air? (Assume the path of the ball in the air approximates a triangle to solve this)
224 Meters
- One side and two angles
- two sides and a non-included angle
Solve to find all unknown angles in △ABC if a = 9, b = 5 and c = 8
C = 62.2 degrees
A = 84.3 degrees
B = 33.6 degrees
For the triangle with side lengths a = 13, b=12 and c = 5, find the Area.
Area = 30