1 vote
If two complementary angles are in the ratio of 2 : 3, find the ratio of the square of the smaller angle to the square of the greater angle.
If two complementary angles are in the ratio of 2 : 3, find the ratio of the square of the smaller angle to the square of the greater angle.
1). 3 : 2
2). 9 : 11
3). 4 : 5
4). 4 : 9
1 answers
1 vote
Let the two complementary angles be 2x and 3x.
We know that the sum of complementary angles = 90o
⇒ 2x + 3x = 90o
⇒ x = 90°/5 = 18o
The smaller angle = 2 × 18 = 36o
The greater angle = 3 × 18 = 54o
The ratio of the square of the smaller angle to the square of the greater angle = 362 : 542 = 4 : 9
∴ The ratio of the square of the smaller angle to the square of the greater angle = 4 : 9