Question

the diagonal of a rectangle makes an angle of 48degree with its smaller side. if the length of the smaller side it's 16cm what is the length of greater side
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Answer 1

Length of rectangle is 17.776 cm and diagonal of rectangle = 23.916 cm.

Step-by-step explanation:

1. Let

  Breadth of rectangle = B = 16 cm

  Length of rectangle = L  

  Diagonal of rectangle = D

2. Given Angle between diagonal and breadth is 48°

   \mathbf{\sin 48=0.743}sin48=0.743

  So

  \mathbf{\cos 48=\sqrt{\left ( 1-\sin ^{2}48 \right )}=0.669}cos48=(1−sin248)=0.669

  We can write

  \mathbf{\tan 48=\frac{\sin 48}{\cos 48}=\frac{0.743}{0.669}=1.111}tan48=cos48sin48=0.6690.743=1.111

3. From trigonometry ratio

   \mathbf{\tan 48=\frac{Length}{Breadth}=\frac{L}{6}}tan48=BreadthLength=6L

  So  

  Length of rectangle \mathbf{L=\tan 48\times 16=1.111\times 16=17.776 cm}L=tan48×16=1.111×16=17.776cm

4. Again from trigonometry ratio

   \mathbf{\cos 48=\frac{Breadth}{Diagonal}=\frac{16}{D}}cos48=DiagonalBreadth=D16

  So

  Diagonal of rectangle \mathbf{D=\frac{16}{\cos 48}=\frac{16}{0.669}=23.916 cm}D=cos4816=0.66916=23.916cm

Step-by-step explanation:

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