Right Angled Triangle

Formulas and definitions

Sine Rule

Cosine Rule

Area

100

If side AB is 3 cm and side BC is 8 cm, what is the measure of angle C, to the nearest degree?

21°

100

Define the ratios for sine, cosine and tangent in terms of Opposite, Adjacent and Hypotenuse

sinθ =O/H

cosθ =A/H

tanθ =O/A

100

State the sine rule

Sine law: A/SinA = B/SinB = C/SinC

100

State the cosine rule

a^2 = b^2 + c^2 -2bc(CosA)

100

If b=3 and h=4, A=?

What is A=6

200

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?

55°

200

Define tangent in terms of other trigonometric functions

Tanθ = sinθ /cosθ

200

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

200

Determine side a in △ABC to one decimal, if ∠B = 130˚, b = 50mm, and c=20mm.

a = 34.8mm

200

Write the formula for the area of a triangle in terms of A, b and c

Area = 1/2*b*c*sinA

300

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˚

300

Explain how both sine and cosine functions are represented on the unit circle

sinθ = y axis value,

cosθ = x-axis value

300

△ABC with ∠A = 44˚, ∠B = 56˚, and b=17m. Find the remaining unknowns

∠C = 80˚ c = 20.2m a = 14.2m

300

In triangle ABC, C=37º, a=8 and b=11.Find the length of side c

c=6.7

300

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

54cm^2

400

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˚

400

In what two situations can the cosine rule be used

- two sides and an included angle are given

- three sides are given

400

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

400

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˚

400

Write a derivation of the formula:

Area = 1/2*b*c*sinA

See derivation on the board

500

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

500

In what two situations can the sine rule be used

- One side and two angles

- two sides and a non-included angle

500

Solve △ABC, a=6, b=10, and A=42˚, how many triangles can be formed? Explain.

No triangles can be formed.

500

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

500

For the triangle with side lengths a = 13, b=12 and c = 5, find the Area.

Area = 30

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