Rhombus MATH

Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120°

Correct answer:

m =  2.3094 cm

Step-by-step explanation:

$$\begin{gathered} u=4\text{ cm } \\ 1.MT;\mathrm{\mid }MT\mathrm{\mid }=u=4cm \\ 2.S;S\in MT;\mathrm{\mid }SM\mathrm{\mid }=\mathrm{\mid }ST\mathrm{\mid } \\ 3.p;p\perp MT;S\in p \\ 4.\mathrm{\sphericalangle }TAX;\mathrm{\sphericalangle }TAX=30\mathrm{°} \\ 4.\mathrm{\sphericalangle }MTY;\mathrm{\sphericalangle }MTY=30\mathrm{°} \\ 5.H,A=p\cap AX;TY \\ 6.MATH \\ m=u\mathrm{/}2\mathrm{/}\sin 60\mathrm{°}=\sin \pi \mathrm{/}3=2.309=2.3094\text{ cm} \end{gathered}$$

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Solustion2

Constructions steps:

1. make angle XAY = 120 deg
2. draw its axis p througth point A....
3. draw two paralels lines l1,l2 to axis p at distance 4/2 = 2 cm
4. intersections of legs of angle XAY and l1, l2 is points is points M and T.
5. make point H - use symmetry of point A in mirror of line MTrhombus

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