Question

the diagonal of a rectangle makes an angle of 48 degree with smaller side if the length of the smaller side is 16 cm what is the length of Great asset bracket sin 48 degree equal to zero point 743​

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°

   $\mathbf{\sin 48=0.743}$

  So

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

  We can write

  $\mathbf{\tan 48=\frac{\sin 48}{\cos 48}=\frac{0.743}{0.669}=1.111}$

3. From trigonometry ratio

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

  So  

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

4. Again from trigonometry ratio

   $\mathbf{\cos 48=\frac{Breadth}{Diagonal}=\frac{16}{D}}$

  So

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