Question

R Q TT 6 The diagram shows a sector, POR, of a circle, centre 0, with radius 8 cm and sector angle radians. The lines OR and OR are perpendicular 3 and OPQ is a straight line. Find the exact area of the shaded region. ​

Answer 1

Answer:

Perpendicular - Definition with Examples

Two distinct lines intersecting each other at 90° or a right angle are called perpendicular lines. Example: Here, AB is perpendicular to XY because AB and XY intersect each other at 90°. Non-Example: The two lines are parallel and do not intersect each other.

Answer 2

Answer:

The diagram shows a sector POQ of a circle of radius 10 cm and centre O. Angle POQ is 2.2 radians. QR is an arc of a circle with centre P and POR is a straight line.

i. Show that the length of PQ is 17.8 cm, correct to 3 significant figures.

ii. Find the perimeter of the shaded region.

Solution

i.

Law of Sines;

Therefore, for triangle OQP;

Since we are given that POQ is a sector of a circle of radius 10 cm and centre O;

Since opposite sides of a triangle are equal the corresponding opposite angles are also equal.

Since some of angles of a triangle is equal to rad or ;