Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do I find the point $p$ where the arch meets the red line if the angle of the blue are is known and the height of the yellow?

share|cite|improve this question

If $P(h,k),$ its projection on the bold black line will be $(h,0)$

The the height of the yellow is $k$(known)

The length of the projection on the bold black line will be $h$

So, the tangent of the known angle blue $=\frac kh\implies h=k\cdot$(the cotangent of the angle blue)

share|cite|improve this answer

Well the $y$ coordinate is obviously the height of the yellow line, so that is something we know.

For the $x$ coordinate we can use the tangent. Let $\alpha$ be your angle. It holds that $\tan(\alpha)= \frac{\text{height of the yellow line}}{\text{distance from the center to the yellow line in x direction}}$

As "distance from the center to the yellow line in x direction" equals the $x$ coordinate of P we have

$x = \frac{1}{\tan(\alpha)}\cdot \text{height of the yellow line}$

So P has the coordinates P($\frac{1}{\tan(\alpha)}\cdot \text{height of the yellow line}, \text{height of the yellow line}$)

All this assumes, that the middle of the circle has the coordinates (0,0). Otherwise just shift the result.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.