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Say I've got a rectangle measuring $140$ cm (height) x $300$ cm (width). What is the distance from the top left corner, to the bottom right corner? And whats the formula for calculating the distance?

Also: What is the angle in degrees of the line drawn between the two corners?

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You can just use the Pythagorean theorem for this: $d$=$\sqrt{140^2+300^2}$. The angle in the bottom right corner is given by $\theta$=$\tan^{-1}$$140\over300$ or about 25 degrees. –  user3180 Apr 17 '11 at 23:25

2 Answers 2

You need the Pythagorean theorem. The distance is $\sqrt{140^2+300^2} \approx 331$ The angle from the horizontal to the diagonal (note you need two lines to define an angle) is $\frac{180}{\pi}\arctan(\frac{140}{300})$ assuming your source of arctangents gives radians. If not, delete the $\frac{180}{\pi}$ multiplier (that is just the radian to degree conversion)

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The Pythagorean Theorem: Given a triangle with sides $a$ and $b$, the hypotenuse ($c$) is $c = \sqrt{a^2+b^2}$.

The angle is given by $\arcsin{\frac{a}{c}}$ where $a$ is the opposite side and $c$ is the hypotenuse. (See this image: http://en.wikipedia.org/wiki/File:Trigono_sine_en2.svg)

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