Question

How do find M and N​

Answer 1

option D

Explanation:

In the right angled triangle , one vertex angle is 60° . The other vertex angle will be = 180 - (90+60) = 30°

Hypotenuse = m ; Perpendicular = n ; Base = 4

Side opposite to 60° = Base

Side adjacent to 60° = Perpendicular

Side opposite to 30° = Perpendicular

Side adjacent to 30° = Base

So,

`\sin(60) = (opposite)/(hypotenuse) = (4)/(m)`

`= > ( √(3) )/(2) = (4)/(m)`

`= > m = (4 * 2)/( √(3) ) = (8)/( √(3) )`

Rationalising the value of m gives
`(8 √(3) )/(3)`

Also,

`\tan(30) = (opposite)/(adjacent) = (n)/(4)`

`= > (1)/( √(3) ) = (n)/(4)`

`= > n = (4)/( √(3) )`

Rationalising the value of n gives
`(4 √(3) )/(3)`