Answer:
TRIGONOMETRY
1. Explain the Law of Cosines by ∆ ABC
\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}
a
2
=b
+c
−2bc(cosA)
b
=a
−2ac(cosB)
c
+b
−2ab(cosC)
2. Explain Law of Sines by ∆ ABC
\sf{{\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}}}
sinA
=
sinB
sinC
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.
#LetTheEarthBreathe
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Answers & Comments
Answer:
TRIGONOMETRY
1. Explain the Law of Cosines by ∆ ABC
\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}
a
2
=b
2
+c
2
−2bc(cosA)
b
2
=a
2
+c
2
−2ac(cosB)
c
2
=a
2
+b
2
−2ab(cosC)
2. Explain Law of Sines by ∆ ABC
\sf{{\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}}}
a
sinA
=
b
sinB
=
c
sinC
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.
#LetTheEarthBreathe