Isosceles Triangle

• Nov 6th 2013, 10:50 PM
Cake
Isosceles Triangle
Hey Guys!

Just to be sure. I don't know if I am correct since I can't view the answer on the back of the book

An isosceles right triangle has a hypotenuse of length
10 cm. How long is each leg?

So I have an isosceles triangle

one 90 degree angle and two angles with the same measure.

hypotenuse is 10 so i assume 10^2 = 100

others are 5√2 (bootleg radical sign) I think since I have the hypotenuse of a 45 45 degree right angle has a base of x and hypotenuse x√2.

Not sure if this is correct.
• Nov 6th 2013, 11:44 PM
psimian
Re: Isosceles Triangle
yup, there's a couple ways to do this, both based on the Pythagorean formula.

A^2+B^2=C^2

where C is the hypotenuse, A and B are the legs.
But, since the triangle is isosceles, A=B, so

2*A^2=C^2
substituting...
2*A^2 = (10)^2 = 100
A^2 = 50 = 25*2
A= 5*sqrt(2)

or, if you happen to know that the sides of a 45-45-90 triangle have the ratio 1:1:sqrt(2), you can jump straight to
A*sqrt(2) = 10
A = 10/sqrt(2) = 5*sqrt(2)
• Nov 7th 2013, 12:05 AM
Cake
Re: Isosceles Triangle
Perfect, got it.