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In ΔABC measure of angle B is 90°, if sin A = 24/25, and AB = 1.4 cm, then what is the length (in cm) of side BC?
- A4.8
- B5
- C3
- D5.6
Answer not set
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CCommunity
Sin A = 24/25
⇒ BC/AC = 24/25
⇒ BC = 24k and AC = 12k
Now, by Pythagoras theorem in triangle ABC
⇒ AB2 + BC2 = AC2
⇒ (1.4)2 + (24k)2 = (25k)2
⇒ 1.96 + 576k2 = 625k2
⇒ 49k2 = 1.96
⇒ k2 = 1/25
⇒ k = 1/5
Now,
∴ BC = 24k = 24 × (1/5) = 4.8 cm
⇒ BC/AC = 24/25
⇒ BC = 24k and AC = 12k
Now, by Pythagoras theorem in triangle ABC
⇒ AB2 + BC2 = AC2
⇒ (1.4)2 + (24k)2 = (25k)2
⇒ 1.96 + 576k2 = 625k2
⇒ 49k2 = 1.96
⇒ k2 = 1/25
⇒ k = 1/5
Now,
∴ BC = 24k = 24 × (1/5) = 4.8 cm