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HonourableDragon6239

Hi, I did the steps for this question with what you previously told me to follow. I am not sure if I did it right. Could you please help me? Thank you

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AnanasSuperbe6429

Hi HonourableDragon6239,

Thank you for your question :)

Most of your process is good! Here are a few things I’d like to point out:

I think there’s a miscalculation in your use of the quadratic formula when you calculate a. The equation you're solving is correct, which is why I believe it’s just a small mistake in the calculation. For reference, my value for a is 61.80 m. This will also affect other results you calculated later in the problem, such as the length of the long base of the trapezoid.
I might be using a slightly different method than you to find the length of the small base, but here’s what I did: first, we don’t know much about the right triangle formed by the x-axis, the origin, and the top vertex of the trapezoid (the small base). The only thing we know is the angle, 75°/2, which allows us to write the equation: tan(37,5)=y/x, where (x,y) is the coordinate of the top vertex of the trapezoid. Since you also have the equation of the ellipse and this equation, you can solve them together to find the values of x and y. The y-coordinate corresponds to the distance between the x-axis and the summit of the trapezoid, so that gives you half the length of the small base.
Finally, you don’t need to calculate the height of the trapezoid, since it’s already given in the problem (the altitude corresponds to the height here).

With these small corrections, you should be able to get the right answer :)

Don’t hesitate if you have more questions!

Sandrine

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