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Find, correct to the nearest degree, the three angles of the triangle with the given vertices. P(3, 0), Q(0, 2), R(5, 4) 

          Find, correct to the nearest degree, the three angles of the
triangle with the given vertices. P(3, 0), Q(0, 2), R(5, 4)

Added by Annette P.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find, correct to the nearest degree, the three angles of the triangle with the given vertices. P(3, 0), Q(0, 2), R(5, 4)
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Transcript

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00:01 I have the equation and this i need to find correct to the nearest degree the three angles of triangle with the vertices okay, so if we draw it roughly x comma y this is 0 b3 .0 q0 2 and r is 5 .4 somewhere here will be the r okay so if i write this p q r let us start with finding out angle p according to cosine formula cosine of angle p will be equal to pq squared okay pq squared so i need to first find lengths pq q q r and r p so length of pq according to pythagoras theorem in this right angle three squared 2 square under root under root of 13 and qr is 5 minus 0 whole square according to distance formula and 4 minus 4 minus 2 whole square 25 plus 9 4 29 under root and third is pr so 5 minus 3 2 square plus 4 square and the root of 20 now cosine p according to the formula cosine root is pq square so under root of 13 whole square plus pr square under root of 20 whole square minus q r square divided by 2 into under root 13 into under root 20 13 minus 29 divide by 2 under root 13 under root 20 4 divide by 2 under root 13 under root 20 so they see 2 divide by under root 13 divide by under root of 20 0 .124 so angle p a cos inverse 0 .124 82 .87 498 degrees i will be approximating this afterwards cosine of p we have to find now cosine of q cosine of q that is this angle means pq square plus qr square so pq square is under 13 whole square which is 13 qr 29 minus it will be 20 divide by like this so 13 plus 29 plus 29 minus 20 divide by 2 divide by under root 13 divide by under root of 29 0 .56652 so q will be cos inverse 0 .566 52 which is 54 point 55 point 49147 degrees now angle r will be 306 180 degree minus these two angles 180 degree minus 82 .87498 82 .87498 degrees and plus 55 .49 1477 degrees and plus 55 .491477 degrees 802 .82 .87498...
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