Two chords

From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.

Correct answer:

t =  6.9282 cm

Step-by-step explanation:

D=8 cm A=60 B=A/2=60/2=30 r=D/2=8/2=4 cm  r2=r2+t22 r t cosB t2=2 r t cosB t=2 r cosB=2 r cos30 =2 4 cos30 =2 4 0.866025=6.928=6.9282 cm



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
See also our right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Triangle's centroid
    triangles_1 In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
  • Viewing angle
    zorny The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
  • Two chords
    chords_1 In a circle with a radius of 8.5 cm, two parallel chords are constructed, the lengths of which are 9 cm and 12 cm. Find the distance of the chords in a circle.
  • Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  • Chord MN
    lyra_tetiva Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
  • A trapezoid
    lichobeznik A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48° and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
  • Inner angles
    triangle_1111 The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
  • Triangle SAS
    triangle_iron Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Two groves
    hajovna Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
  • Right angle
    rt_triangle_1 In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
  • Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  • Rhomboid
    triangle-ssa The rhomboid sides' dimensions are a= 5cm, b = 6 cm, and the angle's size at vertex A is 60°. What is the length of the side AC?
  • Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  • Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  • The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  • Triangle from median
    triangles_1 Calculate the perimeter, content, and magnitudes of the triangle ABC's remaining angles, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.