In the Triangle BCD, Angle B is 90° since tangent and radius are perpendicular to one another.
Now, let's find Angle C using Angle sum property of a triangle.
Now, we know that Angle made by an arc on the centre is twice the Angle made by same arc on boundary of circle, hence we can infer that :
So, the required value of x is 9
Your answer is 8.16 miles. 2/3 times 7 + 1/2 times 7 = 8.166666666
Check the picture below.
make sure your calculator is in Radian mode, since the angle is in radians.
in case you're wondering, in the Unit Circle, the radius is 1, and due to that, the arc's length, in this case an arc of 2 units, is the same value as the angle it makes in radians, so, if the arc is 2, then the angle it makes, in this case clockwise, in the direction as a clock moves, or a negative angle of -2 radians then.
4 + 12 + 36... etc
is a sum that can be rewritten in form
4 ( 1, 3, 9, 27, 81, etc) this can further be written in sigma notation:
4 Sigma [ 3 ^ ( i - 1)]
The sum of the indefinite summation will be the limit as i goes to infinity = infinity
