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TRIGONOMETRY

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1.) Explain the Law of Cosines by ∆ ABC

  • [tex]\begin{gathered}\sf{{a ^ 2 = b ^ 2 + c ^ 2 - 2bc(cos A)}}\\ \sf{{b ^ 2 = a ^ 2 + c ^ 2 - 2ac(cos B)}} \\ \sf{{c ^ 2 = a ^ 2 + b ^ 2 - 2ab(cos C)}}\end{gathered} [/tex]

2.) Explain Law of Sines by ∆ ABC

  • [tex]\sf{{\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}}}[/tex]

3.) Explain The SSA ( There is no SSA postulate so you may have just typed the question incorrectly or you may be asking about SSA Possibilities.)

» SSA ( Side-Side-Angle) · the two triangles are equal if two sides and an angle not included between them are equal.

The SSA Possibilities:

  • If ∠A is an acute angle and a≥b, then there is exactly one solution.

  • If ∠A is an obtuse or a right angle and a≤b, then there is exactly no solution.

  • If ∠A is an acute angle, a<b, and a=b sin A then there is exactly one solution.

  • If ∠A is an obtuse or a right angle and a>b, then there is exactly one solution.

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WindyMint

Question :

Law of Cosines by ∆ ABC

[tex] \\ \\ [/tex]

Answer :

[tex] \\ [/tex]

Law of Cosines by ∆ ABC:

Let three side be :

  • a
  • b
  • c

[tex] \\ [/tex]

Formula:

  • a² = b² + c² – 2bc (cos A)
  • b² = a² + c² – 2ac (cos B)
  • c² = b² + a² – 2ba (cos C)

[tex] \\ [/tex]

Also known as :

Law of Cosines by ∆ ABC is also known as :

  • cosine rule

[tex] \\ [/tex]

Define :

The law of cosines states that if any two sides(i.e a , b , or c) of a triangle and angle formed between them ( i.e ∠A , ∠B or ∠C) are give then we are able to find third side.

(side 1)² = (side 2)² + (side 3)² - 2 side 1 × side 2 (cos angle formed between side 2 and side 3)

[tex] \blue{ \huge \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

Question :

Law of Sines by ∆ ABC

[tex] \\ \\ [/tex]

Answer :

[tex] \\ [/tex]

Law of sines by ∆ ABC:

Let three side be :

  • a
  • b
  • c

[tex] \\ [/tex]

Formula :

[tex] \boxed{ \rm \frac{a}{ \sin(A) } = \frac{b}{ \sin(B) } = \frac{c}{ \sin(C) } }[/tex]

[tex] \\ [/tex]

Define :

It is ratio between side of triangle (i.e a , b , c) and sin of angle formed (angle A , angle B or angle C) opposite to it. Above formula you can see side a is side angle and opposite angle sin i.e A are in ratio and they are equal to ratio of side b and sin of opposite angle to b i.e angle B.

[tex] \blue{ \huge \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

Correct Question :

Explain SSA

[tex] \\ [/tex]

Full form

S - Side

S - Side

A - Angle

[tex] \\ [/tex]

Define :

This condition is seen when two triangles are congruent , when two sides are equal and angle which is not formed between them are equal.

[tex] \\ [/tex]

Congruent triangles :

Congruent triangles are those triangles that have exact shape and size.

[tex] \\ [/tex]

Conditions for congruent triangles :

  • SAS

Side - angle - side

  • ASA

angel - side - angle

  • SSA

side side angle

  • SSS

side side side

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