Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9.

Determine the size of the angles of the triangle ΔABC.

Result

A =  27.69 °
B =  27.69 °
C =  124.62 °

Solution:

x=1802+2+9=1801313.8462  A=2 x=2 13.8462=3601327.692327.69274132"x=\dfrac{ 180 }{ 2+2+9 }=\dfrac{ 180 }{ 13 } \doteq 13.8462 \ ^\circ \ \\ A=2 \cdot \ x=2 \cdot \ 13.8462=\dfrac{ 360 }{ 13 } \doteq 27.6923 \doteq 27.69 ^\circ \doteq 27^\circ 41'32"
B=2 x=2 13.8462=3601327.692327.69274132"B=2 \cdot \ x=2 \cdot \ 13.8462=\dfrac{ 360 }{ 13 } \doteq 27.6923 \doteq 27.69 ^\circ \doteq 27^\circ 41'32"
C=9 x=9 13.8462=162013124.6154124.621243655"C=9 \cdot \ x=9 \cdot \ 13.8462=\dfrac{ 1620 }{ 13 } \doteq 124.6154 \doteq 124.62 ^\circ \doteq 124^\circ 36'55"



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Check out our ratio calculator.
See also our trigonometric triangle calculator.

 

 

Next similar math problems:

  1. Clock hands
    clocks Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.
  2. Inscribed triangle
    obluk To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
  3. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  4. Ruler and compass
    triangle_bac Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
  5. Semicircle
    tales-de-mileto In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
  6. Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  7. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  8. Internal angles
    triangle_5 Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
  9. A triangle
    triangle1_1 A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
  10. Triangle SSA
    trojuhol Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
  11. Angles in triangle
    trigonometry The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
  12. Triangle 42
    triangle2_4 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
  13. Reference angle
    anglemeter Find the reference angle of each angle:
  14. The angles
    trojuholnik The angles in the triangle are in the ratio 12: 15: 9. Find the angles.
  15. Median
    tazisko The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
  16. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?