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H ypotenuse length = O pposite side length / S ine of the angle. Hypotenuse = Opposite sinθ H y p o t e n u s e = O p p o s i t e sin. . θ or in example, c = a sin60° c = a sin. . 60 °. H ypotenuse length = A djacent side length / C osine of the angle. Hypotenuse = Adjacent cosθ H y p o t e n u s e = A d j a c e n t cos.
Formula to calculate a side of triangle with given angle. 2. ... Calculate length of arc of circle with ...
For the ABC triangle, I know all the points. From them I calculate the length of all sides. Then I use the cosine theorem to calculate the angle at point A, which is the same as at triangle ACD. And then I use the sine theorem to calculate the length of CD and AD. And from the length of these two sides, I calculate the coordinates of point D ...
If you want to calculate the third side of the triangle, you need more information than simply two sides. For example, if you know the triangle is a right triangle, or if you know the measure of the included angle between the two known segments, then you can determine the length of the third side.
Lubin suggested using the Cosine Law for the first calculation and the Sine Law for the second. This is faster than Cosine Law done twice. The suggestion is to use the Cosine Law to determine the angle opposite a largest side. Then we will know that the other angles are acute, so Sine Law goes smoothly. This works for all triangle types ...
I would like to calculate the length of the side in red on the image. I tried the Law of cosines , but maybe i haven't applied the formula right, because for a side "a" and "b" of size 64 and a angle of 120, the result is 39.
Bisect the angle to get 2 right triangles with known hypotenuse and angles, then use $\sin$ to get the sides opposite the $22.5/2$ degree angles.
$\begingroup$ That's a different story, then you need trigonometry, namely the sine rule: the ratio between the sine of an angle and the length of the opposite side is the same for all the angles in the triangle.
You can indeed find the third side of the right triangle with the following formula: $$\sqrt{2 a^2} = \sqrt{c^2}$$ $$\sqrt{2} a = c$$ Both sides having the same length allows you to turn the sum into a product, which you can partially calculate the square root of.
Adding this as an addendum: since a triangle is uniquely determined (up to a direct or indirect congruence) by its side lengths, you can, in principle, express the inradius (and, indeed, any triangle quantity) in terms of these quantities.