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 answer:

d₁ =  15.7602 cm

Step-by-step explanation:

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

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