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.

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)≐15.7602=15.76  cm a = 10 \ cm \ \\ A = 76 \ ^\circ \ \\ A_{ 2 } = A ^\circ \rightarrow 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) \doteq 15.7602 = 15.76 \ \text{ cm }

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