Question

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

Answer 1

hii!!

given that two complementary angles are in ratio 2 : 3

let the two complementary angles be 2x and 3x.

we know that the sum of two complementary angle is 90°

therefore 2x + 3x = 90°

==> 5x = 90°

==> x = 90/5

==> x = 18

hence, smaller angle = 2x

= 2 × 18

= 36°

greater angle = 3x

= 3 × 18

= 54°

we have to find the ratio of square of smaller angle to square of greater angle.

square of smaller angle = 36² = 1296

square of greater angle = 56² = 3136

now, their ratio :-

1296 : 3136

= 648 : 1568

= 324 : 784

= 162 : 392

= 81 : 196

hope this helps..!!

Answer 2

Heya ✋

Let see your answer !!!

Let the two complementary angles be 2x and 3x. Then,

2x + 3x = 90

=> 5x = 90

=> x = 90/5

=> x = 18

Hence , smaller angle = (2 × 18)° = 36°

greater angle = (3 × 18)° = 54°

Ratio of their squares

= 36^2 / 54^2

= 1,296/2,916

= 4/9

= 4:9





Thanks :))))