A trapezoid

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.

Correct result:

b =  23.094 cm
d =  26.9127 cm
c =  5.1356 cm

Solution:

a=36.6 cm α=60 β=48  h=20 cm  sinα=h:b  b=h/sin(α)=20/sin(60)=23.094 cm
sinβ=h:d  d=h/sin(β)=20/sin(48)=26.9127 cm
x1+c+x2=a cosα=x1:d=x1:26.9127=0 cosβ=x2:d=x2:26.9127=0  c=ad (cosα+cosβ)=ad (cos60 +cos48 )=36.626.9127 (cos60 +cos48 )=36.626.9127 (0.5+0.669131)=5.136=5.1356 cm



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



Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert length units?
See also our right triangle calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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

Related math problems and questions:

  • 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)
  • Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
  • IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 40 cm and legs 22 cm long.
  • Triangles
    triangles_6 Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
  • 30-60-90
    30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
  • 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.
  • 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.
  • Parallelogram
    rovnobeznik_1 Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A.
  • Diagonal BD
    trapezium_right Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42°
  • Paper box
    cuboid_5 Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m2 of the paper consumed 100 such boxes?
  • Four sides of trapezoid
    lichobeznik Calculate the area of the ABCD trapezoid with sides a = 65 cm, b = 29 cm, c = 40 cm, d = 36 cm
  • Parallelogram +ľ
    rovnobeznik_2.JPG | AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
  • The bases
    rr_lichobeznik The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
  • SAS triangle
    triangles2 The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
  • The staircase
    schody The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
  • Elevation angles
    mountain From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
  • Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.