Question

The two angles of a right angled triangle other than 90° are in the ratio 2 : 3. Express the given situation algebraically as a system of linear equations in two variables and hence solve it.

Answer 1

Let the other two angles be x and y in a right-angled triangle, where one angle is 90° and the sum of the other two angles must equal 90°.

x + y = 90°    ...(1)

Given `x/y = 2/3`

3x = 2y

3x − 2y = 0    ...(2)

From equation (1)

x + y = 90

x = 90 − y    ...(3)

Substitute the value of x in equation (2)

3(90 − y) − 2y = 0

270 − 3у − 2y = 0

270 = 5y

y = `270/5`

y = 54

From equation (3)

x = 90 − 54

x = 36

∴ x = 36°, y = 54°