Projection of oblique segment onto another

Question

How can I find the length of segment a, given the length of segment b, and given that the angle between a and b is x?

Alternatively, how can I find the length of segment a, given r and angle y?

OBS: segments r and b are perpendicular.

score 4 · Answer 1 · answered Jun 21 '17 at 09:55

4

(a) You cannot find $a$ with only $b$ and $x$ given. There are infinitely many possible figures can be drawn.

(a) You cannot find $a$ with only $y$ and $r$ given. Again, there are infinitely many possible figures can be drawn.

answered Jun 21 '17 at 09:55

CY Aries

23,393

score 3 · Accepted Answer · answered Jun 21 '17 at 09:51

3

It's impossible to express a in terms of x and b or y and r. You need 3 of them.

answered Jun 21 '17 at 09:51

MeMyselfI

1,135
5
22

1

Those are what i used? There is also $a= r / \sin(90-x+y) * \sin(y)$ – MeMyselfI Jun 21 '17 at 09:54
1

Thank you, that's what I was looking for. – mgiordi Jun 21 '17 at 09:55

score 3 · Answer 3 · answered Jun 21 '17 at 09:51

For the second problem -- given $y$, $r$, $b$, and $r$ and $b$ perpendicular, find the length of segment $a$ -- there is no solution. In particular, there may be two different lengths $a$ that satisfy the question asked, as in the following diagram, where both $u$ and $v$ are possible solutions:

Projection of oblique segment onto another

3 Answers3