SOLUTION: Please help me solve this question: The diagonal of a rectangle are 10cm long. They intersect at an angle of 120 degrees. Make a sketch of the rectangle. Use trigonometry to calcul

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Question 865591: Please help me solve this question: The diagonal of a rectangle are 10cm long. They intersect at an angle of 120 degrees. Make a sketch of the rectangle. Use trigonometry to calculate the perimeter of the rectangle.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
They also intersect at 60 degrees. This makes four isosceles triangles having non-base sides of 5 cm. each. If you focus on the 120 degree isosceles, its equal base angles each are 30 degrees. Now, focus on just ONE half of the rectangle and the triangle formed as half the rectangle. This is a right triangle of hypotenuse 10 cm, and angles are 30, 60, 90. This right triangle is theoretically half of an equilateral triangle. The short side is 10%2F2=5 cm. The long side, all it a, is related as 10%5E2=5%5E2%2Ba%5E2. Solve for a.

Now, having the long side a and short side 5, you can find perimeter:
2a%2B2%2A5=perimeter.