What is the length of the leg of a 45°-45°-90° triangle with a hypotenuse length of 11?

2 Answers
Mar 1, 2018

7.7782 units

Explanation:

Since this is a #45^o-45^o-90^o# triangle, we can determine two things first of all.
1. This is a right triangle
2. This is an isosceles triangle

One of the theorems of geometry, the Isosceles Right Triangle Theorem, says that the hypotenuse is #sqrt2# times the length of a leg.
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#h = xsqrt2#
We already know the length of the hypotenuse is #11# so we can plug that into the equation.
#11=xsqrt2#
#11/sqrt2=x# (divided #sqrt2# on both sides)
#11/1.4142=x# (found an approximate value of #sqrt2#)
#7.7782=x#

Mar 1, 2018

Each leg is #7.778# units long

Explanation:

Knowing that two angles are equal to #45°# and that the third is a right angle, means that we have a right-angled isosceles triangle.

Let the length of the two equal sides be #x#.

Using Pythagoras's Theorem we can write an equation:

#x^2 +x^2 =11^2#

#2x^2 = 121#

#x^2 = 121/2#

#x^2 = 60.5#

#x = +-sqrt(60.5)#

#x = +7.778" "or" " x= -7.778#

However, as sides cannot have a negative length, reject the negative option.