Answer:
4.62 units
Step-by-step explanation:
Let's first find the length OR.
OR² = BR² + OB²
OR² = 5² + 12²
OR² = 25 + 144
OR² = 169
[tex] OR = \sqrt{19} [/tex]
OR = 13
Let's find the area of triangle OBR.
Using the formula :
½bh
Where
b = BR
h = OB
Therefore, area of triangle OBR =
½ * BR * OB
= ½ * 5 * 12
= 30
From the diagram, triange OBR and OAR are parallel to each other, and they equal.
Thus, area of OBR = area of OAR
To find the length PA, we have :
Area of OAR = ½ * OR *PA
Let's make PA subject of the formula:
[tex] PA = \frac{area of OAR}{\frac{1}{2} * OR}[/tex]
[tex] PA = \frac{30}{\frac{1}{2} * 13}[/tex]
PA = 4.618 ≈ 4.62
PA = 4.62 units
