Figure 6 shows a semicircle pts with center o and radius 8cm. qst is a sector of a circle with center s and r is the midpoint of op.[use=3.142]calculate(a)< tor, in radian(b) length, in cm, tq curvepls meee thnkyu

(a) <TOR=pi/3 radians

To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:

|OT|=radius=8cm and |OR|=radius/2=4cm

and can use the sine:

and since <TRO=pi/2, it must be that

(b) The arc length is approximately 7.255 cm

In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.

Towards determining angle <OST:

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can  determine angle <OTS:

and so the angle <OST is

Towards determining |TS|:

Use cosine:

Finally, we can determine the arc length QT:

idc

step-by-step explanation:

idk

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: