Question

In ΔOPQ, o = 9.2 cm, p = 2.4 cm and ∠Q=37°. Find the length of q, to the nearest 10th of a centimeter.

Answer 1

The length of q, to the nearest 10th of a centimeter is 7.6 cm.

Given in question,

In ΔOPQ,

o = 9.2 cm

p = 2.4 cm

∠Q = 37°

Cosine formula ⇒ cos θ = $\frac{o^{2}+p^{2}-q^{2} }{2op}$

Putting the values in equation,

       cos 37 = $\frac{(9.2)^{2}+(2.4)^{2}-q^{2} }{2*9.2*2.4}$

         0.799 = $\frac{84.64 + 5.76-q^{2} }{44.16}$

0.799*44.16 = 90.4 - $q^{2}$

         32.28 = 90.4 - $q^{2}$

                $q^{2}$ = 90.4 - 32.28

                $q^{2}$ = 58.12

                 $q = \sqrt{58.12}$

                 $q = 7.63$

q = 7.6 cm (to nearest 10th)

Hence, length of q is 7.6 cm.

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