Question 114
If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is
Solution
PQRS is rhombus. Let 'O' be the point of intersection of diagonals where the angle is 90°
∠PQO =∠PQR/2 = 60°
∠OPQ = 180° - ∠POQ - ∠PQO = 180° - 90° - 60° = 30°
In ΔPOQ: sin30° = OQ/PQ => OQ = 3 cm
Therefore QS = 2*OQ = 6cm
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