The rhomboid sides' dimensions are a= |AB|=5cm, b = |BC|=6 cm, and the angle's size at vertex A is 60°. What is the length of the diagonal AC?

Correct answer:

AC =  9.54 cm

Step-by-step explanation:

a=5 cm b=6 cm α=60   β=180α=18060=120   cos α = a1:b sin α = h:b  a1=b cosα=b cos60° =6 cos60° =6 0.5=3 cm h=b sinα=b sin60° =6 sin60° =6 0.866025=5.19615 cm  a2=a+a1=5+3=8 cm  AC2 = a22 + h2  AC=a22+h2=82+5.19622=91=9.54 cm

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