1. ## Trigonometry

A player is at position P, such that PBF = 85 degrees and PFB = 25 degress.

Calcualte
the distance PF,
the distance PA,
the triangle APB.

Completely lost with this... grateful for any help.

2. Originally Posted by Ryannnn

A player is at position P, such that PBF = 85 degrees and PFB = 25 degress.

Calcualte
the distance PF,
the distance PA,
the triangle APB.

Completely lost with this... grateful for any help.
Hi Ryannnn,

Use the Law of Sines first to get PF. The other angle you need in triangle is angle PBF which is 70 degrees.

$\frac{\sin 85}{PF}=\frac{\sin 70}{28}$

$PF=\frac{28 \sin 85}{\sin 70}$

Use PF along with AF which is 35.4 and the included angle F (25 degrees) and apply the Law of Cosines.

$(AP)^2=(AF)^2+(PF)^2-2(AF)(PF)\cos F$

$(PA)^2=35.4^2+\left(\frac{28 \sin 85}{\sin 70}\right)^2-2(35.4)\left(\frac{28 \sin 85}{\sin 70}\right)\cos 25$