In - ABC- if - C - 90- - A - 30- c - 20- then the values of a and b are

∠ c = 90^∘, ] ∠ A = 30^∘, c = 20, then a= c sin A/sin C = 10 and b = c sin B/sin C = 10 √(3). Trick : Since the angles are 30^∘, 60^∘, 90^∘ therefore sides mus ...

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Standard XIII

Mathematics

Sine Rule

In Δ ABC, if ...

Question

In $Δ A B C, i f ∠ C = 90^{\circ}, ∠ A = 30^{\circ}, c = 20$ , then the values of a and b are

$10, 10$

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$10, 10 \sqrt{3}$

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$5, 5 \sqrt{3}$

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$8, 8 \sqrt{3}$

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Solution

The correct option is B
$10, 10 \sqrt{3}$

$∠ c = 90^{\circ},] ∠ A = 30^{\circ}, c = 20, t h e n a = \frac{c s i n A}{s i n C} = 10 a n d b = \frac{c s i n B}{s i n C} = 10 \sqrt{3} .$
Trick : Since the angles are $30^{\circ}, 60^{\circ}, 90^{\circ}$
therefore sides must be $1 : \sqrt{3} : 2. H e n c e, a = 10, b = 10 \sqrt{3} .$

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