Step-by-step explanation:
If you recall SOH CAH TOA, you know that
cosine ∠T = adjacent / hypotenuse
You can write this with adjacent = OT and hypotenuse = BT.
And you can also write this with adjacent = AT and hypotenuse = CT.
So cosine ∠T = OT/BT = AT/CT.
But this is not exactly what has to be proven. If we multiply left and right by BT/AT we do get what we want:
[tex]\frac{OT}{BT} \cdot \frac{BT}{AT} = \frac{AT}{CT} \cdot \frac{BT}{AT}[/tex]
OT/AT = BT/CT
which IS what had to be proven.
