rectangle question!!!!!!!!!!!!!!!!!!

Question

"The diagonal of a rectangle is 10- cm long. It makes an angle of 36 degrees with one of the sides. Calculate the area of the rectangle.

Answer 1

The diagonal of a rectangle is 10 cm and angle 36°

Here length AB = DC, width AD = BC and BD = 10 cm

sin36° = opposite side / hypotenuse

sin36° = AD/BD

Trigonometric table in sin36°= 0.5877, cos36°= 0.8090

0.5877 = AD/10

Multiply each side by 10.

AD = 10(0.5877)

AD = 5.877.

cos36° = adjacent side / hypotenuse

cos36° = AB/BD

0.8090 = AB/10

Multiply each side by 10.

AB = (10)0.8090

AB = 8.090

Therefore length AB = DC = 8.090 and width AD = BC = 5.877

The area of the rectangle is A =  length x width sq.cm

A = 8.090 x 5.877 = 47.54493 square. units.