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SL 3.2—2d and 3d trig, sine rule, cosine rule, area - IB Questionbank | RevisionDojo

Practice SL 3.2—2d and 3d trig, sine rule, cosine rule, area with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

Given the triangle ABC where $A C=5 \mathrm{~cm}, B C=4 \mathrm{~cm}, A B=6 \mathrm{~cm}$ .

Find $\angle B$ .

[3]

Find area of the triangle $A B C$ .

[3]

Question 2

SLPaper 2

For the triangle $\mathrm{ABC}, \angle A=30^{\circ}, \mathrm{BC}=4, \mathrm{AC}=6$ . Find the possible value of $\angle B$ and corresponding values of side length of AB

[7]

Question 3

SLPaper 1

Given the diagram of the quadrilateral ABCD with $\mathrm{AD}=5$ .

Find the exact area of the triangle $ABD$ .

[2]

Exact length of $BD$ .

[3]

Find the exact value of $\sin \angle C D B$ .

[3]

Question 4

SLPaper 2

Given the triangular farm ABC with $\mathrm{AB}=12, \mathrm{AC}=20$ and $\angle B A C=35^{\circ}$ . Now there lies a point X on AC such that $\mathrm{AX}: \mathrm{XC}$ is 1:4 as shown in figure. The fencing has to be installed around its perimeter.

Find the total length of the fencing required.

[3]

Now B connects to X making a new farm. Calculate the area of triangle BXC.

[4]

Question 5

SLPaper 2

Two observation towers, $A$ and $B$ , stand on level ground 250 m apart.
Tower $A$ is 40 m high, tower $B$ is 70 m high.
A drone $D$ is observed simultaneously from the tops of both towers.
From $A$ , the angle of elevation of $D$ is $25^\circ$ ; from $B$ , the angle of elevation is $38^\circ$ .
The horizontal bearing of $B$ from $A$ is $090^\circ$ .
The bearing of the drone from $A$ is $042^\circ$ , and from $B$ is $330^\circ$ .

Draw a clearly labelled 3-D diagram showing the towers, the ground separation, the bearings, and the line of sight from each tower to $D$ .

[2]

Let the point vertically below the drone be $P$ on the ground.
Find the horizontal distances $AP$ and $BP$ .

[3]

Hence find the height of the drone above the ground and its straight-line 3-D distance from the top of tower $A$ .

[3]

The drone now circles tower $A$ at constant height $106.3$ m, describing a horizontal circle of radius 200 m.
A camera on $A$ can rotate through a maximum of $160^\circ$ before needing to reset.
Determine the length of visible path of the drone from $A$ before the camera must reset, giving your answer to the nearest metre.

[2]

During this circular motion, the drone begins a climb such that its height increases proportionally to the square of the horizontal angle turned:
$h(\theta) = 106.3 + 2.5\theta^2 \quad (0 \le \theta \le 2.7925),$ where $\theta$ is in radians.
Find, correct to three significant figures,

the total 3-D distance flown by the drone over this visible path, and
the greatest angle of elevation of the drone from the top of tower A.

[5]

Question 6

SLPaper 1

Find the side length a using the sine rule.

[3]

Question 7

SLPaper 1

Find the side length a using the cosine rule.

[3]

Question 8

SLPaper 2

Given the triangle $ABD$ with $\mathrm{AB}=13, \mathrm{AD}=6.5$ and there is a point $C$ that lies on line $BD$ such that $\mathrm{BC}=\mathrm{AC}=7$ .

Find $\angle ACB$ .

[3]

Find $\angle CAD$ .

[4]

Question 9

SLPaper 2

For the triangle $\mathrm{ABC}, \angle B=30^{\circ}, \mathrm{AB}=6, \mathrm{AC}=3 \sqrt{2}$ .

Find the area of both possible triangles for $ABC$ .

[5]

Question 10

SLPaper 2

Given the triangle ABC with $\mathrm{AB}=7, \mathrm{BC}=5$ , find the difference between area of both possible triangles for ABC.

[7]

SL 3.2—2d and 3d trig, sine rule, cosine rule, area Questionbank