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  cosA2/2=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}



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