A rhombus

A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.

Correct result:

d1 =  15.76 cm

Solution:

a=10 cm A=76 ∘ A2=A∘→ rad=A∘⋅ π180 =76∘⋅ 3.1415926180 =1.32645=19π/45  cos⁡A2/2=d1/2a  d1=2⋅ a⋅ cos⁡(A2/2)=2⋅ 10⋅ cos⁡(1.3265/2)=15.76 cma=10 \ \text{cm} \ \\ A=76 \ ^\circ \ \\ A_{2}=A ^\circ \rightarrow\ \text{rad}=A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =76 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =1.32645=19π/45 \ \\ \ \\ \cos A_{2}/2=\dfrac{ d_{1}/2 }{ a } \ \\ \ \\ d_{1}=2 \cdot \ a \cdot \ \cos(A_{2}/2)=2 \cdot \ 10 \cdot \ \cos(1.3265/2)=15.76 \ \text{cm}

Try another example


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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert length units?
See also our right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


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

Next similar math problems:

  • 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°.
  • Diagonal
    rhombus Can a rhombus have the same length diagonal and side?
  • Diagonals of the rhombus
    kosostvorec_3 How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  • Diagonal
    diamond Can be a diagonal of diamond twice longer than it side?
  • Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  • Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  • Cosine
    cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
  • The Eiffel Tower
    Eiffel-Tower-Paris The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
  • ABCD
    trig_1 AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
  • Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  • 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 ’?
  • Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  • The spacecraft
    Sputnik_670 The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a
  • Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  • The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  • 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.
  • 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.