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If P is a point on the altitude AD of th...

If `P` is a point on the altitude AD of the triangle ABC such the `/_C B P=B/3,` then AP is equal to `2asinC/3` (b) `2bsinC/3` (c) `2csinB/3` (d) `2csinC/3`

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We can create a diagram using the given details.
Please refer to video to see the diagram.
From the diagram,
`/_ABP = (2B)/3 and /_APB = 90+B/3`
In `Delta APB`,
`(AP)/(sin((2B)/3)) = c/(sin(90+B/3))`
`=>(AP)/(2sin(B/3)cos(B/3)) = c/(cos(B/3))`
`=>AP = 2csin(B/3)`
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