Thread: 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.

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

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?

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.

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

Originally Posted by Rimas

What?

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

oops i misread the question, the diagram show AX = 8 hmm so..

Hello, 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.

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