Can you help me to work out the length of the sides of this triangle?

Question

I am only asking this because I don't remember any high school maths...

I have a triangle, which is an isosceles triangle with a 60cm base. I don't know any of the lengths of the other sides, but I know it is a right angle triangle with 90 degree angle opposite the base and the other two angles 45 degrees each.

Is it possible to calculate the length of the two other sides of the triangle that are the same length without knowing anything more about it?

Excuse me if I'm being really stupid here...

Answer 1

Yes it is possible. Here's how:

Use the pythagorean theorem, you know that

x^2+y^2=z^2

z=60 and x=y

x^2+x^2=3600

2x^2=3600

x^2=1800

x = sqrt(1800)

x=30*sqrt(2)

Answer 2

Flippant answer: Yes, it is possible.

Longer answer, probably closer to what you had in mind:

It's a 90-45-45 isosceles triangle.  The base, which is the long side, is 60cm. If you flip the triangle up on one leg, so that you are looking at it as a right triangle instead of an isosceles triangle, you might see (if you know your sin-cos-tan rules) that a side opposite a 45 angle has a length of 60cm*sin 45. (sin 45 is sqrt(2)/2 )

Alternately, if you don't know them, you've probably been taught that the long side of an isosceles right triangle is sqrt(2) times one of the short sides. Thus, 60 = L * sqrt(2),

and L = 60/sqrt(2).

Thus, the answer is 30 * sqrt (2).

Answer 3

ok, so think of it this way.

a 45-45-90 triangle is a special right triangle.

the rule for these triangle is that the two lengths adjacent to the 45 degree angles are the same and the lenght opposite to the 90 degree angle is that length times the square root of two.

so if the base is 60 cm, then the height is 60 cm too.

this means that the last side is 60 times the square root of 2.