Posted by **sophie** on Sunday, May 22, 2011 at 2:34pm.

Is it possible for the lengths of a right triangle to form a geometric sequence? If yes, determine the lengths and the measures of the acute angles. if it's not possible, explain why not.

- math -
**bobpursley**, Sunday, May 22, 2011 at 3:21pm
lengths of a right triangle? You mean the three sides?

Try it: lengths a, ar, ar^2

now see if Pythagoras postulate will work:

c^2=a^2 + b^2

Either a, or ar^2 is c. Try a first

a^2=(ar)^2+(ar^2)^2

dividing by a^2

1=r^2 + r^4

r^4+r^2-1=0

r^2 = (1+-sqrt(5))/2

r= 1.272

so sides are a; 1.272a; 1.618a

which means a was not the longest side.

check:

(1.618^2)=1^2+1.272^2

acute angles?

sinA= 1.272/1.618 Then B: sinB=1/1.618

## Answer this Question

## Related Questions

math - What are the measures of the angles of a right triangle with side lengths...

tricky math - consider the right triangle with sides 3,4,5. Notice that the ...

Geometry - Tell if the measures 9,11, and 7 can be side lengths of a triangle. ...

Math - Examine the given right angle triangle. Are the side lengths given in the...

Math - True or false and if false write a true statement 1. A right triangle has...

math - What are the measures of the angles of a right triangle with side lengths...

geometry - find the value of x in each triangle: triangle x has 1 angle at 53 ...

geometry - find the value of x in each triangle: triangle x has 1 angle at 53 ...

Math - Determine the number of triangles that could be drawn with the given ...

Math - Determine the number of triangles that could be drawn with the given ...