IB Mathematics Analysis and Approaches Topic SL…

The given diagram shows a circle with center O and radius $r$ . The angle AOB is $\theta$ radians.

Find the value of $\theta$ , in each of the following three cases :

Given that the area of the triangle OAB is equal to the shaded area.

Given that the ratio of the lengths of two arcs (minor AB to major AB ) is $1: 5$ .

Given that the ratio of the shaded area to the non-shaded area is $1: 5$

The diagram shows a sector of a circle with centre $O$ and radius $r$ cm. The area of the sector is $16\pi$ cm $^2$ and the length of the arc is cm.

Points $A$ and $B$ lie on a circle with centre $O$ and radius $r$ cm, where radians. This is shown on the following diagram.

A hot-air balloon $P$ is anchored by two ropes to points $A$ and $B$ on level ground. The distance $AB$ is 75 m. The balloon is vertically above , and in the horizontal triangle .

Find the value of $r$ .

Find the angle of the sector in radians.

Determine the value of $r$ .

Hence, calculate the perimeter of sector $OAB$ .

Determine the value of $r$ .

Hence, calculate the perimeter of sector $OAB$ .

Draw a fully-labelled 3-D diagram showing $A,B,P_0,P$ and all the given angles.

Let $AP_0=x$ m and $BP_0=y$ m. Show that $x\tan28^\circ = y\tan37^\circ$ .

Using the cosine rule in triangle $ABP_0$ , write an equation relating $x$ and $y$ .

Find the height $h$ of the balloon, to the nearest metre.

Now suppose instead that $P_0$ moves horizontally on a circle of radius $75\text{ m}$ centered at $A$ . Find the central angle (radians) and the length of the arc (metres) when the bearing of $P_0$ from changes from to .

If $T_A = k|AP|$ and $T_B = k|BP|$ , find .

IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 3.4—circle, Radians, Arcs, Sectors Questionbank