what is the

Right-angled Triangles

@lhmaths: Lesley Hall

Objective: To use ratios of corresponding sides in right-angled triangles.

What is the oppositeadjacent

ratio for a 600 right-angled triangle?

600

4.5cm

2.7cm

Label the opposite and

adjacent sides.

Label the opposite and

adjacent sides.

opp

adj

oppositeadjacent

=

4.5

2.7

= 1.7(to 1 decimal place)

All the “600“right-angled triangles will be similar – so the

ratio will be 1.7 for all your triangles.

All the “600“right-angled triangles will be similar – so the

ratio will be 1.7 for all your triangles.

similar triangles have all corresponding

angles equal

similar triangles have all corresponding

angles equal




600

x

5cm

600

600

x

3cm 12cm

x

oppositeadjacent

= 1.7

We know that

for these triangles.

opp

opp

opp

adj

adj

adj

x5

= 1.7

x5

= 1.7

x = 8.5cmx

x3

= 1.7

x3

= 1.7

x = 5.1cmx 12x

1.7

7.1cm = x

=

12x

1.7

=




Answers for 400 triangles:

oppositeadjacent

= 0.8

Qus 1: x = 0.8 x 8 = 6.4cm

Qus 2: x = 9 ÷ 0.8 = 11.25cm

y

17cm

10cm

What’s the size of angle

y?

What’s the size of angle

y?

y = 600y = 600




The ratio we have been working out is called the

Tangent Ratio.

The ratio we have been working out is called the

Tangent Ratio.

As long as we know the tangent ratio for a particular right-angled triangle we can calculate sides and angles.

We can look up tangent ratios for different angles using the following table.


Degrees 41 42 43 44 45Tangent 0.8693 0.9004 0.9325 0.9657 1.0000Degrees 51 52 53 54 55Tangent 1.2349 1.2799 1.3270 1.3764 1.4281Degrees 61 62 63 64 65Tangent 1.8040 1.8807 1.9626 2.0503 2.1445Degrees 71 72 73 74 75Tangent 2.9042 3.0777 3.2709 3.4874 3.7321






Degrees 41 42 43 44 45Tangent 0.8693 0.9004 0.9325 0.9657 1.0000Degrees 51 52 53 54 55Tangent 1.2349 1.2799 1.3270 1.3764 1.4281Degrees 61 62 63 64 65Tangent 1.8040 1.8807 1.9626 2.0503 2.1445Degrees 71 72 73 74 75Tangent 2.9042 3.0777 3.2709 3.4874 3.7321

Use the table to find:

tan 620

tan 750

tan-1 1.3764

= 1.8807

= 3.7321

= 540

inverse of tan – use to find an

angle

inverse of tan – use to find an

angle




Use the tangent ratio to find x in each of these triangles.Use the tangent ratio to find x in each of these triangles.

x

x x540

270

8.2cm

7cm

6.3cm

4.8cm

10.6cm

Click on a triangle to see the solution for that triangle.

skip solutionsskip solutions





x

540

8.2cm

backback

Tan 540 =opposit

eadjacentop

p

adj

Tan 540 =x

8.2

Tan 540 =x

8.2x x

8.2 x 1.3764 = x

11.3 = x11.3 = x





x

7cm

6.3cm

backback

opp

adj

Tan x0 =opposit

eadjacent

Tan x0 =6.37

Tan x0 = 0.9

x = 420

x = 420





x

270

4.8cm

10.6cm

backback

opp

adj

Tan 270 =opposit

eadjacent

Tan 270 =4.8x

Tan 270 =4.8x

=

x = 9.4cmx = 9.4cm




Using a CalculatorUsing a Calculator

tan 620

tan 750

tan-1 1.3764

= 1.8807

= 3.7321

= 540

We looked these up earlier using a tangent table, but it’s

more convenient to use a calculator.

We looked these up earlier using a tangent table, but it’s

more convenient to use a calculator.

Type:

tan 62 =

tan 75 =

tan-

1

1.3764 =

For tan-1 use your shift or 2nd button

tanshift

what is the

Documents