The measure of the smallest angle of a tree with a hill is 60°.
The measure of the greatest angle of a tree with a hill is 120°.
Given:
A tree on a 30° slope grows straight up.
To find:
The measures of the
greatest and smallest angles the tree makes with the hill.
Solution:
In figure drawn:
[tex]\angle PQR = 30^o[/tex]
AB= Straight three
Construction:
Draw a parallel line CA to QR through point A.
Now,
[tex]\angle PQR = \angle PAC = 30^o\\\\\angle PAC +\angle PAB = 90^o \text{(Complimentary angles)}\\\\\angle PAB = 90^o -\angle PAC\\\\angle PAB=90^o-30^o=60^o[/tex]
The measure of the smallest angle of a tree with a hill is 60°.
[tex]\angle PAB + \angle BAQ= 180^o\text{(Supplementary angles)}\\\\ \angle BAQ= 180^o-\angle PAB \\\\ \angle BAQ=180^o-60^o=120^oC[/tex]
The measure of the greatest angle of a tree with a hill is 120��.
Learn more about complementary and supplementary angles here:
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