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# Area and Trigonometry

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by

## Mr Mattock

on 1 February 2018

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#### Transcript of Area and Trigonometry

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