Question

The difference of two angles of a right angled triangle is 2/3 of a Right angle. find remaining the angles of the triangle in redian and degree​

Answer 1

The two angles are
`75^(o)` (
`(5\pi)/(12)`radians) and
`15^(o)` (
`(\pi)/(12)`radians)

Explanation:

Right angle =
`90^(o)` =
`(\pi )/(2)` radians
Let x = Lesser angle

y = Greater angle

Angles in degrees:

Sum of angles in a right-angled triangle =
`180^(o)`

`x^(o) + y^(o) + 90^(o) = 180^(o)`

`= x + y = 180 - 90`

`= x + y = 90`

`= x = 90 - y` ——(equation i)

`y^(o) -x^(o) =(2)/(3) (90^(o))`

`= y - x = 60` ——(equation ii)

These two equations are linear simultaneous equations, which can be solved by substitution, elimination or graphical method:

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

Expand the brackets by applying the Distributive Law and bring all the like terms together:

`= y - (90-y)= 60`

`= y - 90 + y = 60`

`= y + y = 60 + 90`

`= 2y = 150`

`= y = (150)/(2)`

`= y = 75^(o)`

Substitute this calculated value in any of the equations to determine the value of x:

`x = 90 - 75`

`= x = 15^(o)`

Angles in Radians:

To convert an angle measured in degrees to radians, multiply by
`(\pi )/(180^(o) )`

`= y = 75^(o) .(\pi)/(180^(o))`

Divide both the numerator and denominator by the Highest Common Factor ‘15’:

`= y = (5\pi )/(12)` radians

`x = 15^(o).(\pi )/(180^(o))`

`= x = (\pi)/(12)` radians