In a right isosceles triangle, the tangent of an acute angle equal to 1 always as always each of two acute angles of the same triangle are [tex]45^\circ[/tex] and the value of [tex]\tan45^\circ=1[/tex].
A triangle which have one right angle and sides which makes that right angle are equal to each other.
In a right isosceles triangle, one angle is right angle or [tex]90^\circ[/tex].
Since by angle sum property of triangle the sum of interrior angles of triangle is [tex]180^\circ[/tex], so the sum of rest two angles except the right angle in a right isosceles triangle is [tex]=180^\circ-90^\circ=90^\circ[/tex].
We also know that in triangle, angles opposite of equal sides are also equal.
In right isosceles triangle the adjoint sides with right angle are equal so the opposite angles of them which are the rest two angles of that triangle are equal.
So each angle should be [tex]=\frac{90^\circ}{2}=45^\circ[/tex]
So tangent of each acute angle [tex]=\tan45^\circ=1[/tex]
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