The law of cosines states that, if [tex]\alpha[/tex] is the angle between sides b and c,
[tex]a^2 = b^2+c^2-2bc\cos(\alpha)[/tex]
So, plugging our values, we have
[tex]a^2 = 16+16-2\cdot 4\cdot 4\cdot\cos\left(\dfrac{\pi}{4}\right)[/tex]
This is equal to
[tex]a^2 = 32-32\cdot\dfrac{\sqrt{2}}{2} = 32-16\sqrt{2}[/tex]
The length of a² will be equal to (32 - 16√2).
The triangle in which the two opposite sides are equal and the two opposite angles are equal is called the isosceles triangle.
It is given that in an isosceles triangle abc has a=π/4 and b=c=4. Then the value of a² will be calculated as below:-
Using the cosine formula to calculate the value of a².
a² = b² + c² -2bc cosФ
a² = 16 + 16 - 2(4)(4)cos(π/4)
a² = 32 - ( 32 x {√2/2})
a² = 32 - 16√2
Therefore, the length of a² will be equal to (32 - 16√2).
To know more about the isosceles triangle follow
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