Question

If two tangents inclined at an angle of 120° are drawn to a circle of radius 5cm, then find the length of each tangent.

Answer 1

I think the answer is 10/root 3

Answer 2

so given here it that the tangents are inclined ate an angle of 120 and are drawn to a circle of radius 5cm.

the pair of tangents touches circle at 2 points . So basically we here two 2 right angled triangle . since radius is perpendicular to the tangent.

so the angles are 90, 60, 30
and sin60=√3/2
so the lengths of the tangents is 10/√3
since the tangent is the hypotenuse and radius the opposite side for the angle 60
so but trigonometry sin(60) =opposite/ hypotenuse
5/x=√3/2
therefore x=10/√3 which is the the tangent length .