Diagonals in diamond

In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.

Result

u1 =  160
u2 =  277.13

Solution:

u12=a2+a22aacos60 u12=2a22a2cos60 u1=a2(1cos60)=160u_1^2 = a^2+a^2-2aa \cos 60^\circ \ \\ u_1^2 = 2a^2-2a^2 \cos 60^\circ \ \\ u_1 = a \sqrt{ 2(1-\cos 60^\circ )} = 160
 β=18060=120 u22=a2+a22aacos120 u22=2a22a2cos120 u2=a2(1cos120)=277.13 \ \\ \beta = 180^\circ -60^\circ = 120^\circ \ \\ u_2^2 = a^2+a^2-2aa \cos 120^\circ \ \\ u_2^2 = 2a^2-2a^2 \cos 120^\circ \ \\ u_2 = a \sqrt{ 2(1-\cos 120^\circ )} = 277.13







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




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

Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator.

Next similar math problems:

  1. Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
  2. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles.
  3. 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).
  4. 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
  5. Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
  6. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  7. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  8. 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.
  9. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  10. Heron backlaw
    heron_math Calculate missing side in a triangle with sides 17 and 34 and area 275.
  11. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  12. Four sides of trapezoid
    lichobeznik-stredni_pricka_3 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.
  13. Medians of isosceles triangle
    iso1 The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
  14. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  15. 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?
  16. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  17. 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?