lauril6vara7hle
Answered

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

Answer :

calculista
see the picture attached to better understand the problem

we know that
[tex]AB=4cm \\ AC=4 cm[/tex]

in the right triangle ADB
[tex]angle DBA=angle DAB \\ =45 degrees[/tex]
[tex]cos (DAB)= \frac{AD}{AB} [/tex]
where
AD is the adjacent side angle DAB (altitude)
AB is the hypotenuse triangle ADB 
Angle DAB=[tex]45[/tex]°
so
solve for AD
[tex]AD=AB*cos (45)[/tex]
[tex]AD=4* \frac{ \sqrt{2}}{2} \\ AD=2 \sqrt{2} cm[/tex]

therefore

the answer is 
the length of the altitude is [tex]2 \sqrt{2} cm[/tex]
${teks-lihat-gambar} calculista
oladayoademosu

The length of the altitude drawn from the right angle to the hypotenuse is 2√2 cm

The new triangle

Since in the isosceles right triangle, the length of the altitude drawn from the right angle to the hypotenuse side creates a new right angle with hypotenuse side the length of isoceles right triangle.

Length of altitude

Let

  • h = length of altitude and
  • L = length of leg of isosceles right triangle = 4 cm

Since the altitude bisects the right angle, we have that

cos(90°/2) = h/L

cos45° = h/L

h = Lcos45°

h = 4 × 1/√2

h = 4 × 1/√2 × √2/√2

h = 4√2/2

h = 2√2 cm

So, the length of the altitude drawn from the right angle to the hypotenuse is 2√2 cm

Learn more about isosceles right triangle here:

https://brainly.com/question/3956010

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