Right Angled Triangle
Formulas and definitions
Sine Rule
Cosine Rule
If side AB is 3 cm and side BC is 8 cm, what is the measure of angle C, to the nearest degree?

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

A school soccer field measures 45 m by 65 m. To get home more quickly, David decides to walk along the diagonal of the field. What is the angle of David path, with respect to the 45-m side, to the nearest degree?

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

An 8m ladder is leaning against a vertical wall. The foot of the ladder is 6m from the wall. How far up the wall does the ladder reach and what is the angle of elevation of the ladder?
x= 5.3 m Y = 41˚

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



For a triangle with angle A = 40 Degrees, and sides b = 12cm and c = 14cm, find the Area



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

In what two situations can the sine rule be used

- One side and two angles

- two sides and a non-included angle

Solve △ABC, a=6, b=10, and A=42˚, how many triangles can be formed? Explain.
No triangles can be formed.

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

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