SOLUTION: two angles of a right triangle are complementary and are in the ratio of 1:2 What are the measures of the three angles?

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Question 559122: two angles of a right triangle are complementary and are in the ratio of 1:2 What are the measures of the three angles?
Answer by josmiceli(7363) About Me  (Show Source):
You can put this solution on YOUR website!
The 3 angles must add up to 180 degrees in
any triangle.
It is a right triangle, so 1 of the angles is 90 degrees
Call the other 2 angles a and b
+a+%2B+b+%2B+90+=+180+
+a+%2B+b+=+180+-+90+
(1) +a+%2B+b+=+90+
--------------
given:
+a%2Fb+=+1%2F2+
Multiply both sides by +2b+
(2) +2a+=+b+
Substitute (2) into (1)
(1) +a+%2B+2a+=+90+
(1) +3a+=+90+
(1) +a+=+30+
and, since
(1) +a+%2B+b+=+90+
(1) +30+%2B+b+=+90+
(1) +b+=+60+
The angles are 90, 60, and 30