A rhombus 4

A rhombus has a side length of 10 cm. Find the angles at each corner of the rhombus if the shorter of the two diagonals measures 7 cm. Give your answers to the nearest degree and give clear geometric reasoning at each stage of your solution.

Correct answer:

α =  139 °
β =  41 °
γ =  139 °
δ =  41 °

Step-by-step explanation:

a=10 cm d=7 cm  a2 = (d/2)2+(f/2)2  f=2 a2(d/2)2=2 102(7/2)2=3 39 cm18.735 cm sin φ = d/2 : a φ=π180°arcsin((f/2)/a)=π180°arcsin((18.735/2)/10)69.5127   α=2 φ=2 69.5127=139=139°131"

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