In a circle with an 8-inch radius, a central angle has a measure of 60°. how long is the segment joining the endpoints of the arc cut off by the angle?

The length of segment joining the endpoints of the arc is

Step-by-step explanation:

we know that

In the triangle ABC

see the attached figure to better understand the problem

-----> is the radius of the circle  

----> given problem (central angle)

Initially the triangle ABC is an isosceles triangle

Remember that

the sum of the internal angles of triangle must be equal to

For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to

The equilateral triangle has three equal sides and tree equal angles

so

Hence

The length of segment joining the endpoints of the arc is

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°