Question

The diagonal of a rectangle is 12 cm and makes an angle ${35}^{\circ }$ with one side .Then find the area of the rectangle. $[sin{35}^{\circ }=0.57,cos{35}^{\circ }=0.81]$

Answer 1

Let x and y be the length and breadth of the rectangle respectively.

In right-angled triangle ABC

$sin{35}^{\circ }=\frac{CB}{AC}=\frac{y}{12}\Rightarrow y=12sin{35}^{\circ }$

$y=12\times 0.57=6.84cm$

$cos{35}^{\circ }=\frac{AB}{AC}=\frac{x}{12}$

$x=12cos{35}^{\circ }$

$x=12\times 0.81=9.72$

Area =$x\times y=9.72\times 6.84=66.48c{m}^2$