Question 76

If two complementary angles are in the ratio of 2:3. find the ratio of square of smaller angle to square of greater

Solution

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

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