In - ABC- if a -18- b -24 and c -30 and - C -90- find sin A - sin B and sin C-

A=18, b=24 and c=30 and ∠ c=90^∘ Letsin A/a=sin B/b=sin C/c =sin A/18=sin B/24=sin90/30 =sin A/18=sin B/24=1/30 =sin A/18=1/30⇒ sin A=18/30=3/5 =sin B/24=1/ ...

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Standard XII

Mathematics

Sine Rule

In Δ ABC, if ...

Question

$In Δ A B C, if a = 18, b = 24 and c = 30 and ∠ C = 90^{\circ}, find sin A, sin B and sin C.$

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Solution

$a = 18, b = 24 and c = 30 and ∠ c = 90^{\circ} Let \frac{s i n A}{a} = \frac{s i n B}{b} = \frac{s i n C}{c} = \frac{s i n A}{18} = \frac{s i n B}{24} = \frac{s i n 90}{30} = \frac{s i n A}{18} = \frac{s i n B}{24} = \frac{1}{30} = \frac{s i n A}{18} = \frac{1}{30} \Rightarrow s i n A = \frac{18}{30} = \frac{3}{5} = \frac{s i n B}{24} = \frac{1}{30} \Rightarrow s i n B = \frac{24}{30} = \frac{4}{5} ∴ s i n A = \frac{3}{5}, s i n B = \frac{4}{5}, s i n C = 1$

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Q. In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.

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InΔABC,if a = 18, b = 24 and c = 30 and ∠C=90∘, find sin A, sin B and sin C.

a=18, b=24 and c=30 and ∠c=90∘Letsin Aa=sin Bb=sin Cc=sin A18=sin B24=sin9030=sin A18=sin B24=130=sin A18=130⇒ sin A=1830=35=sin B24=130⇒ sin B=2430=45∴ sin A=35, sin B=45,sin C=1

$In Δ A B C, if a = 18, b = 24 and c = 30 and ∠ C = 90^{\circ}, find sin A, sin B and sin C.$