1.

length and breadth if rectangle paper is in the ratio is √3:1.then what is the angle made by its diagonals​

Answer»

GIVEN :

The RATIO of length and BREADTH of rectangle = L : B = √3 : 1

To Find :

The angle made by diagonals

Solution :

Let The Length = L = √3 x

     The breadth = B = x

From figure ABCD is rectangle

For right angle TRIANGLE Each angle of rectangle = 90°

In Δ  ABC

Sin angle = \dfrac{perpendicular}{hypotenuse}

Or, Sin 90° = \dfrac{AB}{AC}

Or, 1 = \dfrac{x}{AC}

Or, AC = x  

Again

∵  Tan angle  = \dfrac{perpendicular}{base}

Tan\Theta _2 = \dfrac{AB}{BC}

          = \dfrac{x}{\sqrt{3} x}                    

          = \dfrac{1}{\sqrt{3} }

∴  \Theta _2 = Tan^{-1} ( \dfrac{1}{\sqrt{3} } )

       =  30°

For any triangle , sum of all angles = 180°

So,  \Theta _1  = 180° - ( 90° +   \Theta _2 )

            = 180° - ( 90° +   30° )

            = 60°

Hence, The angle of diagonal are 30° , 60°    ANSWER


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