Let ABC be a triangle right-angled at B. If C = 60° and AB = 3 cm, find the BC and AC lengths, respectively.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. √3 cm, 2√3 cm.
We know that
tan θ = P/B
here, P = Perpendicular and B = base
According to the figure
tan 60 = 3/BC [tan60 = √3]
⇒ √3 = 3/BC
⇒ BC = 3/√3
on rationalizing
⇒ BC = 3√3/3 = √3
So, BC = √3 cm
Now, by Pythagoras theorem
⇒ AC2 = AB2 + BC2
⇒ AC2 = 32 + √32
⇒ AC2 = 9 + 3
⇒ AC2 = 12
⇒ AC = 2√3 cm
So, BC = √3 cm and AC = 2√3 cm