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Question

What formula do I use if I have the hypotenuse, but I need to find the length of each leg of isosceles right triangle.

Answer 1

leg² + leg² = hyp²

If the triangle is isosceles, the 2 legs are equal, so you have

2x² = hyp²
x√2 = hyp
x = hyp / √2

Answer 2

c^2 = b^2 + a^2, where c is the hypotenuse and a and b are the 'legs' as you call them.

Since its an isosceles right triangle, the legs are equal, so b = a

therefore c^2 = 2(a^2), so the leg length (a) = sqrt(c^2 / 2)

Answer 3

since it is a rt triangle the angles are 45, 45, and 90.
in a right triangle sin 45 = opposite/hypotenuse therefore a side which are the same for an isosceles triangle is
side=hypotenuse * sin 45(.707)
remember soh cah toa
sin angle = opposite/ hypotenuse
cos angle = adjacent/ hypotenuse
tan angle = opposite/adjacent

Answer 4

c² = a² + b² --- Pythagorean Theorem
Since both legs are the same:
c² = a² + a²
c² = 2a² --- Square root of each side...
c = (√2)a

ANSWER: c = (√2)a --- where c is the hypotenuse, and a is the measure of the two identical legs)

Answer 5

It is also the pythagorean theorem, only with two sides set as equal since it is isoceles:

PYTHAGOREAN: a^2+b^2=c^2
A = B: a^2 + a^2 = c^2
SIMPLIFY: 2a^2 = c^2

Now simply plug in the known hypothenuse value, such as 8.

2a^2 = 8
a^2 = 4
a = 2

The length of the legs in this case is 2.

Answer 6

leg squared + leg squared = hypotenuse squared or

2 leg squared = hypotenuse squared

Answer 7

since it is isosceles, a=b so
h^2=a^2+a^2=2a^2
a=.5h√2