Rhombus diagonals

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

Correct answer:

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

Step-by-step explanation:

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

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

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

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

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