Question

As a part of a campaign, a huge balloon with message of “AWARENESS OF CANCER” was displayed from the terrace of
a tall building. It was held by string of length 8 m each, which inclined at an angle of 60c at the point, where it was tied as
shown in the figure. Calculate -:
i. What is the length of AB ?
ii. If the perpendicular distance from the centre of the circle to the chord AB is 3 cm, then find the radius of the circle.

Answer 1

Answer:

AB = 8 m

Radius = 5 m

Step-by-step explanation:

Consider that in the given figure we mark a centre point of AB. Let us call this as Point C.

Now this will bisect angle APB into tow half such that angle APC is 30 degree.

Now we use the geometric function;

Sin Θ = Perpendicular/ Hypotenuse

Here angle is 30.

Perpendicular =  AC = ??

Hypotenuse = 8

Putting it in formula,

Sin 60 = AC/ 8

AC = 0.5 x 8

AC = 4

Similarly BC will aslo be 4

AB = AC + CB

AB = 8 m

In right angled ACO

OA^2 = AC^2 + CO^2

OA^2 = 4^2 +3^2

OA = 5m

Radius = 5 m

Answer 2

Here is your answer ---@@@-----------@@@@@@@@$$$$$$$$-

In the given figure mark a centre point on line AB as C. Let the center be O.

Now C will bisect angle AOB into tow half such that angle AOC is 30°.

We know that

Sin theta= perpendicular /Hypotenuse

as it get bisected so the angle is 30°.

Perpendicular =  AC = ??

Hypotenuse = 8

Putting it in formula,

Sin 60 = AC/ 8

=>AC = 1/2 x 8

=>AC = 4

Similarly BC is aslo 4

AB = AC + CB

=>AB = 8 m

Now,

In right angled ΔACO

=> OA²= AC² + CO²

=>OA² = 4²+3²

=> OA= √25

=> OA = 5m

Hence, the radius = 5 m.