IB Mathematics Analysis and Approaches Topic SL…

Two boats, A and B, set off from the same point $P$ at the same time. Boat A travels in a straight line at a speed of $40\ \mathrm{km}/\mathrm{h}$ , while boat B moves in a different straight-line direction at $60\ \mathrm{km}/\mathrm{h}$ . The angle between their paths is $60^{\circ}$ .

the distance between the two boats after $1.5$ hours. Give your answer to $3$ significant figures.

(e) 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 .

(f) Using the original position of the balloon, let $T_A=k|AP|$ and $T_B=k|BP|$ , where . Find .

A stained-glass artist is constructing a window in the shape of a square with an equilateral triangle mounted on top. The base of the triangle is the same length as the side of the square, $x$ cm, and fits perfectly along its upper edge, so this shared edge is not part of the outer boundary. The total area of the window is designed to be $500 \text{ cm}^2$ .

(b) Write an expression for the area of the square in terms of $x$ .

(d) Use the total area $500 \text{ cm}^2$ to form an equation and solve for $x$ . Give your answer to 3 significant figures.

(e) Find the total length of the outer boundary (perimeter) of the window. Give your answer to 3 significant figures.

In triangle $ABC$ , $AB = 8$ cm, $BC = 11$ cm, and $A\hat{B}C = 65^\circ$ .

(a) Find the area of triangle $ABC$ .

(b) Find the length of $AC$ .

In a triangular sail, $\triangle ABC$ :

angle $A = 45^\circ$
angle $B = 75^\circ$
side $a = 10$ m

triangle diagram with angles 45° and 75° and side a=10 m

(b) Find the area of the triangle.

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 $P_0$ , and $\angle AP_0B = 60^\circ$ in the horizontal triangle $ABP_0$ .

The angles of elevation of the balloon are $28^\circ$ from $A$ and $37^\circ$ from $B$ .

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

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

(a) an expression for the vertical height of the equilateral triangle in terms of $x$ .

(a) the length of side $b$ using the law of sines.

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

IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

IB Mathematics Analysis and Approaches SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 3.2—2d and 3d Trig, Sine Rule, Cosine Rule, Area Questionbank