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Given and isosceles triangle's side lengths, how to find a base angle when no other angle is given?

User Silvaren
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Explanation:

it does not matter if it is an isoceles triangle or not (isoceles just means both legs are equally long), as soon as we know all sides, we can calculate any of the 3 angles by using the law of cosine (the generalized Pythagoras for any type of triangle) :

c² = a² + b² - 2ab×cos(C)

c is the side with the angle C being opposite to it. a and b are the other 2 sides. when we know all 3 sides, the only variable is C.

2ab×cos(C) = a² + b² - c²

cos(C) = (a² + b² - c²)/(2ab)

C = cos^-1 ((a² + b² - c²)/(2ab))

this works in all cases.

if you want to know a specific angle, you set that angle to be C, the opposite side to be c, and the other 2 sides as a and b.

and that's it.

User Joanne
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