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I have the following geometric shape.

enter image description here

How can I calculate a, b and c?

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    $\begingroup$ You should try to solve it yourself, show part of that and ask question when you could not proceed further. $\endgroup$
    – Narasimham
    Aug 6, 2021 at 17:07

1 Answer 1

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figure with extra notations

I have marked $2$ extra lines on the figure, which form a right angle with $x$. I have also split $a$ into $a_1$ and $a_2$.

The triangle with the yellow line as one of its sides is a right triangle. The yellow line has the same length as $d_1$. Then, we have $\tan(\alpha)=\frac{d_1}{a_1}$, from which its easy to get $a_1$. $a_2$ is equal to $x$, since they are part of a rectangle, so $a=a_1+x$. By Pythagora in the same triangle, we get the length of $c_1$.

The orange line is equal in length to $d_2$. Then in the right triangle we get $\sin(\beta)=\frac{d_2}{c_2}$, from which you can obtain $c_2$, and finally $c$ as $c_1+c_2$.

Finally, we have $\tan(\beta)=\frac{d_2}{x_1}$, and $b=x-x_1$.

I'm sure you can work out the computations!

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    $\begingroup$ Try not to answer questions when someone dumps one here, like the above, with no effort. Apart from being against site policy, it is more helpful to get them to do some work themselves (which is why people often ask "what have you tried?"). Also, it is not unlikely that this is their assessed homework or exam, so giving them the complete answer is unfair to the rest of their class. $\endgroup$
    – user1729
    Aug 9, 2021 at 14:40

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