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Summary Grade 12: Sine, Cosine & Area Rules and Heights and Distances in 2D and 3D $2.91   Add to cart
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Summary Grade 12: Sine, Cosine & Area Rules and Heights and Distances in 2D and 3D
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  • Course
  • Mathematics
  • Institution
  • 12th Grade

All aspects covered in Grade 12 regarding Sine, Cosine & Area Rules and Heights and Distances in 2D and 3D. This document includes: - Cover page - Area Rule - Cosine Rule - Sine Rule - Applications - Heights and Distances in 2D and 3D - includes examples

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Document information

  • May 19, 2022
  • 7
  • 2021/2022
  • Summary

Subjects

  • trig
  • sine rule
  • cosine rule
  • area rule
  • 2dtrig
  • 3dtrig
  • matric
  • heightsampdistances

Written for

  • 12th Grade
  • Mathematics
  • 200
All documents for this subject (421)

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Sine, Cosine & Area
Rule and heights &
distances in 2D & 3D

, Area Rule
GIVEN:
an included angle




BASIC FORMULAE
- in any ABC: △ A
Area ABC = 1 bc sin ^A
2
△
c
^
= 1 ac sin B b
2
= 1 ab sin ^C B C
2 a


PROOF
sin ^
B=h and sin ^C = h A
c b
h1


∴ h = c sin ^B and h = b sin ^C c
Area △ABC = 1 ah
b

2
∴ Area △ABC = 1 ac sin ^B = 1 ab sin ^C B
a h2 C
2 2 d

Similarly using AB as the base and h1 as the height

Area △ABC = 1 ac sin ^B = 1 bc sin ^A
2 2


EXAMPLE
A DETERMINE THE AREA OF △ABC
Area = 1 ac sin ^B
2
65 cm
Area = 1 (33) (65) sin 101,7°
101,7°
C 2
B
33 cm
Area = 1050,2 cm2


When working out an angle, we use normal algebra and
sin-1(..)
NB: remember sin has two solutions

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