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Guest:

P = (−2.55, 0.726), Q = (4.55, 4.79), R = (0.306, 6.36) .
a) Find the angle of vertex P

The following is assuming that the angle is QPR if the vertex is P.

In order to do this, you must first create the vectors <QP> and <QR>

Then, by using the definition of the dot product of two vectors: <QP> • <QR> = |<QP>| * |<QR>| * cos(Θ)
You can find Θ which is the angle you are looking for.
aeccos( (<QP> • <QR>)/( |<QP>| * |<QR>|) ) = Θ = Angle of vertex P

Guest:

P = (−2.55, 0.726), Q = (4.55, 4.79), R = (0.306, 6.36) .
a) Find the angle of vertex P

There are 3 different ways that you can do this.

Method 1: Angle between two lines
tan(<P) = | (m ₂-m ₁) / [ 1+m ₁m ₂ ] |

Where
m ₁ is the gradient of PQ and
m ₂ is the gradient of PR

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Method 2 : Cosine Rule

p ² = q ² + r ² - 2qrCos(<P)

Where
p is QR, q is RP and r is QP

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Method 3 : Using Vectors

Cos(<P) = ( <PQ> · <PR> ) / ( |<PQ>| |<PR>| )

P = (−2.55, 0.726), Q = (4.55, 4.79), R = (0.306, 6.36)
<PQ> = < 4.55 - - 2.55 , 4.55 - 0.726 > = < 7.1, 4.064 >
<PR> = <2.856, 5.634>
<PQ> · <PR> = ( (7.1 x 2.856 + 4.064 x 5.634 ) = 43.174176

|<PQ>| = distance PQ = 8.180837
|<PR>| = distance PR = 6.316541
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No matter which method you choose the answer is still <P = 33 degrees and 20 minutes (to the nearest minute)