# Trigonometry " The Ambiguous Case".

• Nov 8th 2010, 02:04 AM
ejaykasai
Trigonometry " The Ambiguous Case".
So, This is the problem, solve the triangle

Quote:

1. A = 35°
a = 5
b = 8

So it's gonna be like this right?

Quote:

- angle A is Acute
a < b
a__bsinA
5__8sin35°
5>4.59
therefore two triangles.

So This is [COLOR="rgb(46, 139, 87)"]my answer for the 1st triangle.[/COLOR]

Quote:

B = 66.60°
c = 8.54
C = 78.4°

CORRECT ME IF I'M WRONG..
Can anyone teach me how to solve for the other triangle? :|
• Nov 8th 2010, 03:59 AM
earboth
Quote:

Originally Posted by ejaykasai
So, This is the problem, solve the triangle

So it's gonna be like this right?

So This is my answer for the 1st triangle.[/COLOR]

CORRECT ME IF I'M WRONG..
Can anyone teach me how to solve for the other triangle? :|

You have to use the Sine rule (what you obviously did)

1. From $\displaystyle \dfrac{\sin(B)}{\sin(35.8^\circle)}=\dfrac85~\impl ies~\sin(B)\approx 0.9177...$.

2. Since $\displaystyle \sin(B) = \sin(180^\circ - B) \implies B\approx 66.6^\circ~\vee~ B \approx 113.4^\circ$

3. You now can calculate the dimensions of the 2nd triangle.