An isosceles right triangle has leg lengths of 4 centimeters. what is the length of the altitude drawn from the right angle to the hypotenuse?
2 cm
cm
4 cm
cm

Step-by-step explanation:

refer the attached figure .

In ΔABC

∠ABC = 90°

SINCE AB = BC

So, ∠BAC=∠ACB (angles opposite to equal sides are equal

Now using angle sum property of triangle i.e. sum of all angles of triangle is 180°

⇒∠BAC+∠ACB+∠ABC =180°

⇒∠BAC+∠BAC+∠ABC =180° (∠BAC=∠ACB )

⇒2∠BAC+90° =180°

⇒2∠BAC =90°

⇒∠BAC=45°

So, ∠BAC=∠ACB=45°

Now in ΔABD

AB is hypotenuse

BD is perpendicular AD is base

Thus to find BD use trigonometric ratio

Thus the length of BD is

Hence he length of the altitude drawn from the right angle to the hypotenuse is

tangent

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