# Find, correct to the nearest degree, the three angles of the triangle with the given vertices.P(3, 0),      Q(0, 2),      R(5, 5)∠RPQ =°∠PQR =°∠QRP =°

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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, 5)
 ∠RPQ = ° ∠PQR = ° ∠QRP = °
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Step 1

To find the three angles of the triangle formed with the vertices P(3,0), Q(0,2), R(5,5).

Obtain the length of the sides of the triangle PQR using the distance formula as follows. help_outlineImage Transcriptionclose(0-3)' +(2-0) = v9+4 13 ORb(5-0)+(5-2) 25+9= 34 PR= c= {(5-3)+(5-0) /4+ 25 = 29 \Pg=a= fullscreen
Step 2

Find the angles using cosine rule as follows. Obtain the value of angle P as given below. help_outlineImage Transcriptionclosea bc2bccos P bca cos P 2bc 34+29-13 2/986 50 2/986 50 = cos 2/986 =37.23 370 fullscreen
Step 3

Obtain the value of angle Q ... help_outlineImage Transcriptioncloseb2 ac22accosQ ac-b cosQ 2ac 13+29-34 2/377 2/377 cos 2 377 = =78.11 780 fullscreen

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