Rhombus diagonals

In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond

Correct answer:

a =  13 cm
A =  45.2397 °
B =  134.7603 °
S =  120 cm²

Step-by-step explanation:

$$\begin{gathered} e=24\text{ cm } \\ f=10\text{ cm } \\ a=\sqrt{(e\mathrm{/}2{)}^2+(f\mathrm{/}2{)}^2}=\sqrt{(24\mathrm{/}2{)}^2+(10\mathrm{/}2{)}^2}=13\text{ cm} \end{gathered}$$

$$\begin{gathered} \sin A\mathrm{/}2=f\mathrm{/}2:a \\ A=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (f\mathrm{/}2\mathrm{/}a)=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (10\mathrm{/}2\mathrm{/}13)=45.2397\text{°}=45\mathrm{°}14^{\mathrm{\prime }}23\mathrm{"} \end{gathered}$$

$$\begin{gathered} \sin B\mathrm{/}2=e\mathrm{/}2:a \\ B=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (e\mathrm{/}2\mathrm{/}a)=2\cdot {\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arcsin (24\mathrm{/}2\mathrm{/}13)=134.7603\text{°}=134\mathrm{°}45^{\mathrm{\prime }}37\mathrm{"} \end{gathered}$$

$S={\displaystyle \frac{e\cdot f}{2}}={\displaystyle \frac{24\cdot 10}{2}}=120{\text{cm}}^2$

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