Circular railway

The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?

Correct result:

b1 =  103.1095 km

Solution:

c=30 b=95 a=70  s=a+b+c2=70+95+302=1952=97.5 S=s (sa) (sb) (sc)=97.5 (97.570) (97.595) (97.530)672.6522 km2  r=S/s=672.6522/97.56.899 km  R=a b c4 r s=70 95 304 6.899 97.574.1468 km  ΔRRb b2=R2+R22 R2 cosθ  θ=arccos(2 R2b22 R2)=arccos(2 74.146829522 74.14682)1.3906 rad  b1=θ R=1.3906 74.1468=103.1095 km

Try calculation via our triangle calculator.




We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Gardens
    garden The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
  • Compute 4
    14-12-12 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
  • Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  • Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  • Triangular prism
    688_triangle Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm
  • Sides ratio
    triangle3_1 Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
  • Four sides of trapezoid
    lichobeznik2 Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
  • Sides of the triangle
    herons Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
  • Find the area
    triangles_57 Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
  • The farmer
    field_2 The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
  • Cardboard box
    krabicka We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we ca
  • Trapezoid - hard example
    trapezium Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
  • Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  • Park
    park_voda In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
  • Triangle
    triangle_ABC_1 The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
  • Box
    Rhombic_prism Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of are
  • Diamond
    diamond_1 Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.