Additional Mathematics Project PDF

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Additional Mathematics Project Chapter 10: Solution of a triangle ABIGAIL CHIEN

Content 10.1 Sine Rule I.

II.

For the triangle ABC, use the rule, sin rule :

Use the sin rule, angles are given

when one side and two

Given

Given

III.

Use inverted form of sin rule, sides and one non-included angle are given

when two

Given

Given

Facts of triangle  In order to solve a triangle, there must be at least 3 information given  An Included angle is an angle bounded by two sides

10.2 Cosine Rule I.

II.

For the triangle ABC, use the rule, cosine rule :

Use this cosine rule formulae, and an included angle are given

Given

Given

when two sides

III.

Use this cosine rule formulae, are given

when all three sides

Given Given

Given

10.3 Area of Triangles I.

II.

Area of a right angle triangle is :

For any triangle ABC, the formula for the area triangle is :

10.4 Three-Dimensional Geometry

I.

Angle between a line and a plane - the angle between the line AB and the plane is angle AA’B  A’B – Orthogonal projection  AA’ – Normal

II.

Angle between two planes – the angle between the plane WZXY and the plane ABCD is angle PMP’  Angle PMA and MP’B = 90 degrees

Cosine Rule a^2 = b^2 + c^2 -2bc cos A b^2 = a^2 + c^2 -2ac cos B c^2 = a^2 + b^2 -2ab cos C

Sin Rule a/sin A & b/sinB & c/sin C

Area of a triangle Area = 1/2absinC

are all equal

= 1/2bcsinA = 1/2acsinB Solution of triangle

Three-Dimensional Problems  Angle between a Line and a Plane  Angle between Two Planes...