Angle of diagonals

Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°.

Correct answer:

o =  37.2099 cm
S =  75.0724 cm²

Step-by-step explanation:

$$\begin{gathered} u=14\text{ cm } \\ \alpha =130^{\circ } \\ \beta =\alpha \mathrm{/}2=130\mathrm{/}2=65^{\circ } \\ \sin \beta =a:u=12.6883:14=0 \\ a=u\cdot \sin {\beta }^{\circ }=u\cdot \sin 65^{\circ }=14\cdot \sin 65^{\circ }=14\cdot 0.906308=12.68831\text{ cm } \\ \cos \beta =b:u=5.9167:14=0 \\ b=u\cdot \cos {\beta }^{\circ }=u\cdot \cos 65^{\circ }=14\cdot \cos 65^{\circ }=14\cdot 0.422618=5.91666\text{ cm } \\ o=2\cdot (a+b)=2\cdot (12.6883+5.9167)=37.2099\text{ cm} \end{gathered}$$

$S=a\cdot b=12.6883\cdot 5.9167=75.0724{\text{cm}}^2$

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