In an isosceles right triangle, the length of the hypotenuse is 81. Find the length of each leg?

Question

In an isosceles right triangle, the length of the hypotenuse is 81. Find the length of each leg

Answer 1

81^2=2x^2

x=81/sqrt(2)

Answer 2

Since it is an isoceles right triangle, the legs are equal, and therefore Pythagorea's theorem a^2 + b^2 = c^2 would essentially be a^2 + a^2 = 2a^2 = c^2. We know c = 81, therefore

2 a^2 = 81 ^2
2 a^2 = 6561
a^2 = 6561 / 2 = 3280.5
a = sqrt (3280.5) = 57.27

Each leg would measure approx 57.27

Answer 3

Use the Pythagorean theorem:

(a^2 + b^2 = c^2)

You need to take the square of the opposite side and the square of the adjacent side to figure out the hypotenuse.

Because this is an isosceles triangle, the opp. and adj. sides are equal.

First, you will need to divide 81 by 2, which = 40.5.

Then, find the square root of 40.5. This is approximately 6.363.

The other two legs of this triangle are 6.363.

Answer 4

h^2 = a^2 + a^2
since triangle is isosceles, the other sides are equal
2a^2 = 81^2
a^2 = 81^2/2
a = sqrt(81^2/2)
= 9/sqrt(2)

Answer 5

leg = 81*sqrt(2)/2 approx = .707*81 = 57.267

Answer 6

let the length of each leg be x, then

2x^2 = 81
x = 9/sqrt(2) = 6.36

Answer 7

leg^2+leg^2=81^2
2leg^2=6561
leg^2=6561/2
leg=sqrt6561/2=57.276
anther solution
sin45=leg/81
1/sqrt2=leg/81
leg=81/sqrt2