Rhomboid

The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?

Result

|AC| =  6.65 cm

Solution:

sinγsin60=56 γ=arcsin.72168 γ=46.194 β=1806046.194=73.806 AC6sin73.806sin60 AC=61.1088853 AC=6.6533121 cm6.65  cm  \dfrac{ \sin \gamma }{ \sin 60 } = \dfrac{ 5 }{ 6 } \ \\ \gamma = \arcsin .72168 \ \\ \gamma = 46.194^\circ \ \\ \beta = 180-60-46.194 = 73.806^\circ \ \\ \dfrac{ |AC| }{ 6 } \dfrac{ \sin 73.806^\circ }{ \sin 60 } \ \\ |AC| = 6 \cdot 1.1088853 \ \\ |AC| = 6.6533121 \ cm \doteq 6.65 \ \text{ cm } \ \\

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
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. 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).
  2. Mast shadow
    horizons Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
  3. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  4. Height 2
    1unilateral_triangle Calculate the height of the equilateral triangle with side 38.
  5. Two triangles SSA
    ssa Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
  6. Trigonometry
    sinus Is true equality? ?
  7. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  8. Sines
    sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
  9. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  10. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  11. Calculation of CN
    color_combinations Calculate: ?
  12. Trinity
    trojka How many different triads can be selected from the group 43 students?
  13. AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  14. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  15. 75th percentile (quartille Q3)
    statistics Find 75th percentile for 30,42,42,46,46,46,50,50,54
  16. Median and modus
    dice_3 Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
  17. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1