# 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:

$a=10 \ \text{cm} \ \\ A=76 \ ^\circ \ \\ A_{2}=A ^\circ \rightarrow\ \text{rad}=A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =76 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =1.32645=19π/45 \ \\ \ \\ \cos A_{2}/2=\dfrac{ d_{1}/2 }{ a } \ \\ \ \\ d_{1}=2 \cdot \ a \cdot \ \cos(A_{2}/2)=2 \cdot \ 10 \cdot \ \cos(1.3265/2)=15.76 \ \text{cm}$

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.

Tips to related online calculators
Do you want to convert length units?
Cosine rule uses trigonometric SAS 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:

## Next similar math problems:

• 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
Can a rhombus have the same length diagonal and side?
• Diagonals of the rhombus
How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
• Diagonal
Can be a diagonal of diamond twice longer than it side?
• Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
• Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
• Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
• The Eiffel Tower
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
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
• Scalene triangle
Solve the triangle: A = 50°, b = 13, c = 6
• Two groves
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
Calculate the greatest triangle angle with sides 197, 208, 299.
• The spacecraft
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
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
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
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
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.