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maths help!

a parallelogram has sides of lengths 9cm and 7.5cm.
The size of the larger interior angle is theta
Given the area of the parallelogram is 60cm^2 find the exact value of tan theta.

So far I've:
split the parallelogram into two triangles
therefore 30cm^2 = 1/2 x 9 x 7.5 x sin theta.
I used this to find the larger angle and tried to find the tan theta value but im not getting the answer which is 8/17
Reply 1
Original post by caramel:)
a parallelogram has sides of lengths 9cm and 7.5cm.
The size of the larger interior angle is theta
Given the area of the parallelogram is 60cm^2 find the exact value of tan theta.

So far I've:
split the parallelogram into two triangles
therefore 30cm^2 = 1/2 x 9 x 7.5 x sin theta.
I used this to find the larger angle and tried to find the tan theta value but im not getting the answer which is 8/17

Can you upload a pic (link) of the question. If its the larger interior angle, then tan should be negative so ... and arctan(8/17) is about 25 degrees (largest?). For those stats, the parallelogram has vert height of 6 2/3 so the angles are not that far from 90.

I suspect the question is right but the answer is wrong.
(edited 3 months ago)
Reply 2
I agree with Mqbx. In the question you might consider using the other angle and sin and then sorting out tan at the end. That is, if this is a-level.

Also, a rectangle 9 by 7.5 is only 67.5 and so this parallelogram is only a bit off being a rectangle. There is no way that the angle required is what the answer indicates.
Tan theta needs to be negative if it is greater than 90 and less than 180, which it is.

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