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 result:

t =  6.928 cm

Solution:

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 cmD=8 \ \text{cm} \ \\ A=60 \ ^\circ \ \\ B=A/2=60/2=30 \ ^\circ \ \\ r=D/2=8/2=4 \ \text{cm} \ \\ \ \\ r^2=r^2 + t^2 - 2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t^2=2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t=2 \cdot \ r \cdot \ \cos B ^\circ =2 \cdot \ r \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ 0.866025=6.928 \ \text{cm}



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
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

Next similar math problems:

  • 3d printer
    filament 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
  • Car crash
    car1_7 On the road, with a maximum permitted speed of 60 km/h, there was a car crash. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, a
  • Angled cyclist turn
    cyclistTurn The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
  • Iron pole
    ministranti What is the mass of pole with the shape of a regular quadrilateral prism with a length of 1 m and a cross-sectional side length of a = 4.5 cm make from iron with density ρ = 7800 kg/m³?
  • Fighter
    vyskovy uhol A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
  • Iron density
    pipe1_2 Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
  • The copper wire
    cu_wire The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
  • Orlík hydroelectric plant
    1280px-Orlík_1 The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the
  • Cu thief
    trolleywire_1 The thief stole 121 meters copper wire with cross-section area of 103 mm2. Calculate how much money gets in the scrap redemption, if redeemed copper for 4.6 eur/kg? The density of copper is 8.96 t/m3.
  • The water tank
    hydroglobus The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
  • Water level
    bazen_11 How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
  • Heptagonal pyramid
    truncated_hexagonal_pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
  • Pump
    pumpa What power has a pump output to move 4853 hl of water to a height of 31 m for 8 hours?
  • A car
    car_31 A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!
  • Copper sheet
    cuplech The copper plate has a length of 1 m, width 94 cm and weighs 9 kg. What is the plate thickness, if 1 m3 weighs 8715 kg?
  • Friction coefficient
    car What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
  • Density of the concrete
    beton_1 Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.