The approximate measure of angle Q will be 93.2°. Then the correct option is B.
Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
a² + b² – 2ab cos C = c²
In a triangle QRS, the length of QR is 21, the length of RS is 32, and the length of SQ is 23.
Then the approximate measure of angle Q will be given as,
RQ² + SQ² – 2 × SQ × RQ × cos Q = RS²
21² + 23² – 2 × 23 × 21 × cos Q = 32²
441 + 529 – 966 cos Q = 1024
970 – 966 cos Q = 1024
966 cos Q = – 54
cos Q = – 54 / 966
cos Q = – 0.0559
Q = 93.2°
The approximate measure of angle Q will be 93.2°.
Then the correct option is B.
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