If in a triangle A B C- a-6 cm - b-8 cm - c-10 cm- then the value of sin 2 A isA- 6 - 25B- 8 - 25C- 10 - 25D- 24 - 25

The correct option is D 24/25 Given that, a = 6 cm, b=8 cm, c=10 cm ∴ cosA=b^2+c^2 a^2/2ac =(8)^2+(10)^2 (6)^2/2×8×10=4/5 ⇒ sinA=3/5 ∴ sin2A=2 sinA cosA =2×3 ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

If in a trian...

Question

If in a triangle ABC, a=6cm, b=8cm, c=10cm, then the value of sin 2A is

6/25

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8/25

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10/25

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24/25

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Solution

The correct option is D
24/25

Given that, a = 6 cm, b=8 cm, c=10 cm

$∴ c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 a c} = \frac{(8)^{2} + (10)^{2} - (6)^{2}}{2 \times 8 \times 10} = \frac{4}{5} \Rightarrow s i n A = \frac{3}{5} ∴ s i n 2 A = 2 s i n A c o s A = 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25}$

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If in a triangle ABC, a=6cm, b=8cm, c=10cm, then the value of sin 2A is

The correct option is D 24/25 Given that, a = 6 cm, b=8 cm, c=10 cm ∴cosA=b2+c2−a22ac=(8)2+(10)2−(6)22×8×10=45⇒sinA=35∴sin2A=2sinAcosA=2×35×45=2425