Question

Please help I would really appreciate it

Answer 1

The side BA measures 11.53 units long.

Explanation:

Step 1:

The side BP and PC are both the radii of the given circle. In the question, it is given that BP is 6 units long so PC is also equal to 6 units.

The line PA is split into two segments, PC and AC. It is given that AC is 7 units long.

So
`PA = PC+CA = 6+7 =13` units.

Step 2:

The triangle ABP is right-angled. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

`(PA)^(2) = (BP)^(2) + (BA)^(2) .`

Substituting the values we know, we get

`13^(2) = 6^(2) + BA^(2) , BA^(2) = 13^(2) - 6^(2) ,`

`BA^(2) = 169 - 36 = 133,`

`BA = √(133) = 11.5325.`

Rounding off this value, we get BA measures 11.53 units long.