Question

in the given figure O is a tangent to the circle with Centre O such that OT=4 centimetre and angle OTA is 30 degree then find the length of TA.

Answer 1

therefore
seg AT =2√3 cm

Answer 2

Answer:

The length of TA is $2\sqrt{3}cm$

Step-by-step explanation:

TA is a tangent to circle at point A. It means the angle OAT is 90 degree because the radius is perpendicular to the tangent at the point of tangency.

So, triangle OAT is a right angle triangle.

$\cos\theta=\frac{Base}{Hypotenuse}$

$\cos (30^{\circ})=\frac{TA}{4}$

$\frac{\sqrt{3}}{2}=\frac{TA}{4}$

$\frac{\sqrt{3}}{2}\times 4=TA$

$2\sqrt{3}=TA$

Therefore the length of TA is $2\sqrt{3}cm$.