In △ABC, right angled at B, BC = 5 cm, ∠ BAC = 30∘ , find the length of the sides AB and AC.
We are gven
∠ BAC = 30∘ , i.e , ∠A = 30∘
and BC = 5cm
Now sinA = BCAC or sin 30∘ = 5AC
or 5AC = 12 ........ [ ∵ sin 30∘ = 12 ]\
or AC = 2 × 5 or 10 cm
To find AB , we have
ABAC = cos A
or AB10 = cos 30∘
or AB10 = √32
∴ AB = √32 × 10 or 5 √3 cm
Hence, AB = 5 √3 cm and AC = 10 cm