How do you determine the number of possible triangles and find the measure of the three angles given $c = 18, b = 10, m ∠ C = 120$ $c=18, b=10, mangleC=120$ ?

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How do you determine the number of possible triangles and find the measure of the three angles given $c = 18, b = 10, m ∠ C = 120$ $c=18, b=10, mangleC=120$ ?

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Answer 1 · 2017-01-16T21:31:54

The Ambiguous Case applies only to acute given angles; the given angle is obtuse, therefore, only one triangle exists.
Use The Law of Sines to find $B$ $B$
Find A by using $A = 180^{\circ} - C - B$ $A = 180^@ - C - B$

Explanation:

Here is a reference for the Ambiguous Case

Use The Law of Sines to find B:

$\frac{sin (B)}{b} = \frac{sin (C)}{c}$ $sin(B)/b = sin(C)/c$

$sin (B) = sin (C) \frac{b}{c}$ $sin(B) = sin(C)b/c$

$B = {sin}^{- 1} (sin (C) \frac{b}{c})$ $B = sin^-1(sin(C)b/c)$

$B = {sin}^{- 1} (sin (120^{\circ}) \frac{10}{18})$ $B = sin^-1(sin(120^@)10/18)$

$B \approx 29^{\circ}$ $B~~ 29^@$

$A = 180 - 120 - 29$ $A = 180 - 120 - 29$

$A \approx 31^{\circ}$ $A ~~ 31^@$

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How do you determine the number of possible triangles and find the measure of the three angles given $c = 18, b = 10, m ∠ C = 120$ $c=18, b=10, mangleC=120$ ?

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Explanation:

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How do you determine the number of possible triangles and find the measure of the three angles given c=18,b=10,m∠C=120c=18, b=10, mangleC=120?

1 Answer

Explanation:

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How do you determine the number of possible triangles and find the measure of the three angles given $c = 18, b = 10, m ∠ C = 120$ $c=18, b=10, mangleC=120$ ?