# Right Triangles

• Mar 21st 2007, 04:50 PM
Godfather
Right Triangles
In right triangle ABC with right angle ACB,AC=8 inches and BC=6 inches point x in on segment AC equidistant from A and B . Find CX.
• Mar 21st 2007, 05:40 PM
topsquark
Quote:

Originally Posted by Godfather
In right triangle ABC with right angle ACB,AC=8 inches and BC=6 inches point x in on segment AC equidistant from A and B . Find CX.

I'll give you the method.

Note that triangle AXB is isosceles. Thus angle ABX is equal to angle BAX. We can find angle BAX since triangle ABC is right, using the inverse tangent function. We also can find angle ABC because of the same fact. Thus by subtraction we can find angle XBC. We now know the value of the angle opposite the side XC of the right triangle XBC. And we know the length of the side adjacent to the angle. So we can use the tangent function to find the length of XC.

-Dan
• Mar 28th 2007, 04:43 PM
Rimas
Quote:

Originally Posted by topsquark
I'll give you the method.

Note that triangle AXB is isosceles. Thus angle ABX is equal to angle BAX. We can find angle BAX since triangle ABC is right, using the inverse tangent function. We also can find angle ABC because of the same fact. Thus by subtraction we can find angle XBC. We now know the value of the angle opposite the side XC of the right triangle XBC. And we know the length of the side adjacent to the angle. So we can use the tangent function to find the length of XC.

-Dan

What?
• Mar 28th 2007, 05:11 PM
ajacka
easy.. basically, u know that AX and BX are equal, so they r both 8. so then you know 2 sides of the triangle BXC, so all you're left with is do a simple pythagorean theorem. CX^2 = BX^2 - BC^2.
• Mar 28th 2007, 05:58 PM
topsquark
Quote:

Originally Posted by topsquark
I'll give you the method.

Note that triangle AXB is isosceles. Thus angle ABX is equal to angle BAX. We can find angle BAX since triangle ABC is right, using the inverse tangent function. We also can find angle ABC because of the same fact. Thus by subtraction we can find angle XBC. We now know the value of the angle opposite the side XC of the right triangle XBC. And we know the length of the side adjacent to the angle. So we can use the tangent function to find the length of XC.

-Dan

Quote:

Originally Posted by Rimas
What?

Quote:

Originally Posted by ajacka
easy.. basically, u know that AX and BX are equal, so they r both 8. so then you know 2 sides of the triangle BXC, so all you're left with is do a simple pythagorean theorem. CX^2 = BX^2 - BC^2.

Neither AX nor BX are 8. AC = 8 according to the problem statement.

Rimas: Please let me know what part of my solution you didn't understand and I'll explain it in more detail.

-Dan
• Mar 28th 2007, 06:09 PM
ajacka
oops i misread the question, the diagram show AX = 8 hmm so..
• Mar 29th 2007, 06:21 PM
Soroban
Hello, Godfather!

Quote:

In right triangle ABC with right angle ACB,AC=8 inches and BC=6 inches,
point X in on segment AC equidistant from A and B. .Find CX.

Let x = CX. .Then AX = 8 - x.

In right triangle XCB, we have: .x² + 6² .= .BX²

Since BX = AX, we have: .x² + 36 .= .(8 - x)²

Then: .x² + 36 .= .64 - 16x + x² . . 16x = 28 . . x = 7/4