how to calculate the sides and hypotenuse length of the right triangle if I know the bigger side = 60 one angle = 60 second angle = 30 (3rd = 90)
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Some hints: what is the third angle? Draw a picture. Can you spot some symmetry? If not, then decode the following hint with http://www.rot13.com/index.php. But please, spend some time trying first. Ersyrpg gur gevnatyr va gur evtug natyr. Jung vf fb fcrpvny va gur erfhygvat gevnatyr? Gel znxvat hfr bs gur rkgen flzzrgel. |
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You could use the identities $$sin(\theta)=\frac{oposite-side}{hypotenuse} $$ $$cos(\theta)=\frac{adyacent-side}{hypotenuse} $$ In fact you have : $$\sin(60)=\frac{60}{hypotenuse} \Rightarrow hypotenuse = \frac{120}{\sin(60)}=\frac{120}{\sqrt{3}}$$ and $$\cos(60)=\frac{adyacent-side}{hypotenuse} \Rightarrow adyacent-side = \cos(60)\cdot hypotenuse =\frac{60}{\sqrt{3}} $$ |
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Well, you don't even need to assume that the triangle is a right triangle. Simply use the Law of sines: $$\frac{a}{\sin A} \,=\, \frac{b}{\sin B} \,=\, \frac{c}{\sin C} .$$ |
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tan(60) = side1/side2 = 60/side2 => side2 = 60/tan(60) = 60/sqrt(3) = 20sqrt(3) sin(60) = side1/hypotenuse => hypotenuse = 60/sin(60)=120/sqrt(3) = 40sqrt(3) |
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