Similar Triangle Algebra (Really Hard)

[BadAtHw]

Triangle CAT is a right triangle: Line AP is the altitude of triangle CAT. Angle CAT is right. Line TP = X. Line PC = X+7. Angle TAP is right. Angle CAP is right.

What is the measure of X (line TP).

How do you solve this? I know you use Geometric means, but multiplying x to X+7 throws me off.

 

[Mrspi]

Triangle CAT is a right triangle: Line AP is the altitude of triangle CAT. Angle CAT is right. Line TP = X. Line PC = X+7. Angle TAP is right. Angle CAP is right.

What is the measure of X (line TP).

How do you solve this? I know you use Geometric means, but multiplying x to X+7 throws me off.

You'd better recheck what you've typed....if <CAT is a right angle, and AP divides <CAT into two parts, <CAP and <TAP, then CERTAINLY angles CAP and TAP cannot be right angles!!! m<CAP + m<TAP = 90. Each of those angles must be less than 90!!

The altitude to the hypotenuse in a right triangle is the geometric mean between the two parts of the hypotenuse that altitude creates.

If AP is an altitude to hypotenuse CT, then

CP / AP = AP / PT

I think you need to know the length of altitude to AP to solve this problem.....

And x(x + 7) = x^2 + 7x.....

Please recheck the problem and be sure you've typed it correctly, and that you have included all of the given information.