Question

TRIGONOMETRIA-AYUDA!!!

Answer 1

1. Triángulo AMC (teorema de senos)

                       $\dfrac{AM}{\sin(\theta-2\alpha)}=\dfrac{a}{\sin\theta}\\ \\ \\AM=\dfrac{a \sin(\theta-2\alpha)}{\sin\theta}=a(\cos2\alpha-\cot\theta\sin2\alpha)$

2. Triángulo AMP

                                    $\dfrac{AM}{\sin(\theta-\alpha)}=\dfrac{AP}{\sin\theta}\\ \\ \\AP=\dfrac{AM~\sin\theta}{\sin(\theta-\alpha)}\\ \\ \\AP=\dfrac{a\sin(\theta-2\alpha)}{\sin(\theta-\alpha)}$

3. En el triángulo ANP

                                     $AN=AP\cos\alpha\\ \\AN=\dfrac{a\sin(\theta-2\alpha)\cos\alpha}{\sin(\theta-\alpha)}$