SOLUTION: The diagonal of a rectangle is 25 meters long and makes an angle of 36� with one side of the rectangle. Find the area and the perimeter of the rectangle.

Question 714707: The diagonal of a rectangle is 25 meters long and makes an angle of 36� with one side of the rectangle. Find the area and the perimeter of the rectangle.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To find the area and perimeter of the rectangle we will need the length and width of the rectangle. To find the length and width using the given diameter and angle, we will use Trigonometry. Drawing a diagram will help you understand the following.

Let x = the side of the rectangle opposite the 36 degree angle.
The diagonal of the rectangle is the hypotenuse of the right triangle formed by it and the length and the width of the rectangle. The Trig functions whose ratios involve the opposite side and hypotenuse are sin and csc. Since our calculator has a sin button but not a csc button we will use sin. Sin is opposite over hypotenuse so:

Multiplying both sides by 25 we get:

I'll leave it up to you and your calculator to turn this into a decimal.

Let y = the side of the rectangle which is adjacent to the 36 degree angle. The function we will use for this side is cos (because it is adjacent over hypotenuse and because we have a cos button on our calculator). The equation we get is:

Multiplying both sides by 25 we get:

I'll leave it up to you and your calculator to turn this into a decimal.

The perimeter of a rectangle is the sum of all the sides. For this rectangle will be x + y + x + y or 2x + 2y. Use the decimals you found earlier to find the perimeter.

The area of a rectangle is the length times the width. For this rectangle the area will be x*y. Use the decimals you found earlier to find the area.
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