# The diagonal of the triangle is 10 and forms an angle of 36 degrees from one of its sides. find the area of the rectangle.

October 7, 2021 | education

| The area of a rectangle is equal to the product of its length and width:

S = a b.

The diagonal of the rectangle AC divides it into two right-angled triangles. Consider one of them, the ABC triangle. Suppose the angle ∠C is 36 °.

With the help of the cosine tower, you can find the length of the BC side:

cos C = BC / AC;

BC = AC · cos C;

cos 36 ° = 0.809;

BC = 10 0.809 = 8.09 cm.

Behind the sine theorem, you can find the length of the side AB:

sin C = AB / AC;

AB = AC sin C;

sin 36 ° = 0.588;

AB = 10 0.588 = 5.88 cm.

Now let’s find the area of the rectangle:

S = 8.09 5.88 = 47.57 cm2.

Answer: the area of the rectangle is 47.57 cm2.