**Area and Trigonometry**

Starter

Find the area of these triangles:

Examples

Find the area of these triangles:

Using trigonometry for area

How can we find the perpendicular height of this triangle? Hence how can we find the area of this triangle?

**L.O. - Use trigonometry to find area of non-right triangles.**

5 cm

12 cm

13 cm

10 cm

16 cm

10 cm

4 cm

9 cm

Starter

Find the area of these triangles:

5 cm

12 cm

13 cm

10 cm

16 cm

10 cm

4 cm

9 cm

30 cm

2

18 cm

2

6 cm

48 cm

8 cm

23

o

Using trigonometry for area

How can we find the perpendicular height of this triangle? Hence how can we find the area of this triangle?

8 cm

23

o

h

8

= sin 23

h = 8 sin23

12 cm

12 cm

Area = (12)(8 sin 23)

1

2

Using trigonometry for area

The area of a non-right triangle can be given by the formula:

b

x

o

a

b sin x

Area = (a)(b sin x)

Area = ab sin x

1

2

1

2

13 cm

9 cm

107

o

8 cm

11 cm

9

o

Examples

Find the area of these triangles:

13 cm

9 cm

107

o

8 cm

11 cm

9

o

Area = (13)(9) sin 107

Area = 55.9 cm

2

1

2

Area = (8)(11) sin 9

Area = 6.88 cm

2

1

2

Activity

Complete the area of triangles worksheet

Activity

Complete the area of triangles worksheet

(a) 9.58 (b) 44.5 (c) 26.2

(d) 17.3 (e) 63.3 (f) 28.7

Extension

(a) 202.1 (b) 72.2

Plenary

Find the area of the blue shaded segment.

Plenary

Find the area of the blue shaded segment.

Area of sector:

x x 24

= 603.18... cm

120

360

2

Area of triangle:

(24)(24) sin 120

= 249.41.... cm

1

2

Area of Segment =

603.18... - 249.41...

=353.8 cm

2

2

2

**Activities**

**Activity**

Answers

Answers

**Key**

Examples

Examples

**Worked**

Example

Example

**Worked**

Example

Example

2