Four sides of trapezoid

In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.

Correct result:

A =  76.58 °
B =  90 °
C =  90 °
D =  103.42 °

Solution:

a=73.6 b=57 c=60 d=58.6 a2=ac=73.660=685=13.6 A1=arccos((d2+a22b2)/(2 d a2))=arccos((58.62+13.62572)/(2 58.6 13.6))1.3366 A=A1 =A1 180π  =1.3365788376612 180π  =76.58  =76.58=763449"a=73.6 \ \\ b=57 \ \\ c=60 \ \\ d=58.6 \ \\ a_{2}=a-c=73.6-60=\dfrac{ 68 }{ 5 }=13.6 \ \\ A_{1}=\arccos((d^2+a_{2}^2-b^2)/(2 \cdot \ d \cdot \ a_{2}))=\arccos((58.6^2+13.6^2-57^2)/(2 \cdot \ 58.6 \cdot \ 13.6)) \doteq 1.3366 \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =1.3365788376612 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =76.58 \ \ ^\circ =76.58 ^\circ =76^\circ 34'49"
B1=arccos((b2+a22d2)/(2 b a2))=arccos((572+13.6258.62)/(2 57 13.6))1.5708 B=B1 =B1 180π  =1.5707963267949 180π  =90  =90B_{1}=\arccos((b^2+a_{2}^2-d^2)/(2 \cdot \ b \cdot \ a_{2}))=\arccos((57^2+13.6^2-58.6^2)/(2 \cdot \ 57 \cdot \ 13.6)) \doteq 1.5708 \ \\ B=B_{1} \rightarrow \ ^\circ =B_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =1.5707963267949 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =90 \ \ ^\circ =90 ^\circ
C=180B=18090=90C=180-B=180-90=90 ^\circ
D=180A=18076.5803=517150=103.42=103.42=1032512" x=A+B+C+D=76.5803+90+90+103.42=360D=180-A=180-76.5803=\dfrac{ 5171 }{ 50 }=103.42=103.42 ^\circ =103^\circ 25'12" \ \\ x=A+B+C+D=76.5803+90+90+103.42=360

Try calculation via our triangle calculator.




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
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:

  • Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  • Cards
    cards_2 Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab
  • Internal angles
    mo-klm The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Det
  • Trapezium ABCD
    lichobeznik_5 In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
  • Trapezium internal angles
    lichob_2_2 A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
  • Roof
    roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
  • Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  • Triangle from median
    triangles_1 Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
  • Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  • Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  • 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?
  • The angle of view
    pole_1 Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
  • Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  • Vector sum
    vectors The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
  • 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 ’?
  • Triangle ABC
    squares4 Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
  • Reference angle
    anglemeter Find the reference angle of each angle: