A rhombus

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

Correct answer:

d₁ =  15.7602 cm

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ A=76{}^{\circ } \\ {A}_2=A°\to \text{rad}=A°\cdot \frac{\pi }{180}=76°\cdot \frac{3.1415926}{180}=1.32645=19\pi /45 \\ \cos A_2/2=\frac{d_1/2}{a} \\ {d}_1=2\cdot a\cdot \cos (A_2/2)=2\cdot 10\cdot \cos (1.3265/2)=15.7602\text{cm} \end{gathered}$$

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