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

See the diagram enter image description here

Known values are

A: (-87.91, 41.98)
B: (-104.67, 39.85)
C: (-96.29, 40.92)
L: 14.63  // L is OC

Known angles

ADB: 60 deg
BAD: 60 deg
ADF: 10 deg

How to calculate Point F? that is 10 deg from point A.

share|cite|improve this question
L is OC or OE ? – Bhargav Jan 3 '12 at 17:15
Homework assignment? – Hidde Jan 3 '12 at 18:19

Given that two of the angles in $\triangle ABO$ have measure $60°$, $\triangle ABO$ is equilateral. It appears that $C$ is the midpoint of $\overline{AB}$, so $L$ is the length of an altitude of $\triangle ABO$ and the lengths of the sides of the triangle are $\frac{2}{\sqrt{3}}L\approx16.89$. Now, $O$ is $16.89$ from both $A$ and $B$, which gives a system of equations that can be solved for the coordinates of $O$: $(-94.4456,26.4022)$ (as shown in your picture, so I'll use this one) or $(-98.1344,55.4278)$ (which would be above $\overline{AB}$).

Assuming that the arc shown is intended to be circular and centered at $O$, $F$ is the image of $A$ under a $10°$ rotation about $O$, which we can carry out by applying to $A$:

  1. a translation that takes $O$ to $(0,0)$, $(x,y)\to(x+98.1344,y-55.4278)$,
  2. a rotation of $10°$ about the origin, $(x,y)\to(x\cos10°-y\sin10°,y\cos10°+x\sin10°)$, and
  3. a translation that takes $(0,0)$ to $O$, $(x,y)\to(x-98.1344,y+55.4278)$.

Carrying out these transformations on $A$ gives $$F\approx(-90.7144, 42.8782).$$

share|cite|improve this answer

if L is OE then u have the radius,


AF = $\frac{\theta }{2\pi }2\pi r$ where r=L

u know A,O

so solve the 2 equations to get coordinates of F

share|cite|improve this answer
sorry! L is OC. but I can calculate R using R = tan(30) x L – coure2011 Jan 3 '12 at 17:32
can you please explain how to calculate F? I need Fx and Fy! – coure2011 Jan 3 '12 at 17:42

C is exactly the center of AB, so COA = 30 deg. AOF is 10 deg (given), so EOF is 20 deg.

Calculate R using tan(30)•L. Calculate d(F,EO) using R•sin(20).

The entire shape is turned, so turn everything so that OE and the y-axis are parallel.

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.