MPM2D1 Date: ____________ Day 4: Intro to Trig Ratios Chapter 7: Trigonometry of Right Triangles

Page 1 of 4

Triangles & Trigonometry

Trigonometry means _________________________________. It is used to

calculate lengths of _____________ and measures of ______________ in

triangles.

**** Trigonometry is all about________________! ****

Right Triangle Terminology

The three sides to a right-angle triangle are:

1) Hypotenuse – ________________________________

2) Adjacent - _________________________________

3) Opposite – _________________________________

Ex1. In XYZ , identify the hypotenuse, adjacent

side, and opposite side for ________

Hypotenuse:

Adjacent:

Opposite:

Ex2. In XYZ , identify the hypotenuse, adjacent

side, and opposite side for ________

Hypotenuse:

Adjacent:

Opposite:

Opposite and Adjacent sides of a triangle ___________ depending on the ____________ of the

angle in the triangle.

Label the hypotenuse (hyp), opposite (opp) and adjacent (adj) sides for marked angles.

D

F

E

β

β

MPM2D1 Date: ____________ Day 4: Intro to Trig Ratios Chapter 7: Trigonometry of Right Triangles

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Investigation – Developing Primary Trig Ratios

Using a ruler, carefully measure each of the sides of triangles ABC, ADE, AFG, and AHI.

Fill in the table below using millimetres and computing each ratio to 2 decimal places.

adjacent means neighbouring or beside (eg. AB is adjacent to A )

opposite means across from (eg. BC is opposite A )

the hypotenuse is the long side of a right triangle (eg. AC is a hypotenuse)

Triangle

Side

Opposite to

A

Side

Adjacent to

A

Hypotenuse Trigonometric Ratios

∆ABC

BC = AB = AC = ACBC

ACAB

BABC

∆ADE

∆AFG

∆AHI

Explain why triangles ABC, ADE, AFG, and AHI are all similar.

How does this explain the pattern of values in the last three columns?

I

C

E

G

A H F D B

30˚

MPM2D1 Date: ____________ Day 4: Intro to Trig Ratios Chapter 7: Trigonometry of Right Triangles

Page 3 of 4

TRIGONOMETRIC RATIOS

In a right triangle, the three trigonometric ratios for eacn non-right angle are given by:

Hint for remembering the trig ratios:

SOH CAH TOA

Ex: State the three primary trig ratios for the indicated angle in the following triangles.

sin βo=

cos βo=

tan βo=

sin βo=

cos βo=

tan βo=

β

β

MPM2D1 Date: ____________ Day 4: Intro to Trig Ratios Chapter 7: Trigonometry of Right Triangles

Page 362 # 1, 3, 4, 5, 6, 7, 8 Page 4

A) Determine the Ratio (Make sure that your calculator is in degrees)

Determine the following ratios to four decimal places.

sin 36o =

cos 55o =

tan 66o =

tan 6o =

cos 47o =

sin 65o =

B) Determine The Angle (make sure that your calculator is in degrees)

It is relatively straightforward to find the trig ratio knowing the angle, but what if we don’t know the

angle?

We need the inverse (opposite) operation to find the angle.

cos β = 0.8660 swap the ratio and the angle

cos-1 0.8660 = β On the calculator press one of the following (depending on

your brand of calculator): either '2ndF sin' or 'shift sin'.

cos αo = 0.9952

tan βo = 11.4301

tan θo = 1.1918

sin Ω0 = 0.1788

sin αo = 0.9781

Cos βo =0.019