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SL 3.3—Angles of elevation and depression, bearings - IB Questionbank | RevisionDojo

Practice SL 3.3—Angles of elevation and depression, bearings 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

A person is flying their kite. The kite is on a string of length 100 m and has an angle of elevation of $65^{\circ}$ .

Find the height that the kite is flying at above the point the person is holding it.

[2]

Now the second person raises their kite to the same vertical height from the same position as the first person. The angle between two kites is $15^{\circ}$ .

Find the length of the string for the kite flown by the second person.

[3]

Question 2

SLPaper 2

From a given point, the angle of elevation to the top of the building is $25^{\circ}$ . After walking 80 m towards the building, the angle of elevation is now $31^{\circ}$ .

Find x and h in the following figure.

[5]

Question 3

SLPaper 1

Find the bearing of Q from P in the following diagrams.

2. 3. 4. 5. 6.

[6]

Question 4

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 5

SLPaper 2

Given a diagram below in which the tower AB is of length 5 m tall standing on the building. The angle of elevation of the top of the building from C is $45^{\circ}$ and the angle of depression from A to C is $60^{\circ}$ .

Find the height of the building.

[4]

Question 6

SLPaper 2

A person requires rescuing from the top of the building at a height of 8.2 m . A fire truck has an extendable ladder with its fixed end at a height of 1.6 m . It has been parked at a horizontal distance of 3.7 m from the building.

Find the length of the ladder required to reach the top of the building.

[3]

For safety purposes, the angle between the ladder and the horizontal surface it stands on should be between $70^{\circ}$ to $80^{\circ}$ . Determine whether the ladder in this situation would be safe or not.

[4]

The fire truck is moved to a horizontal distance from the building that makes the angle of $72^{\circ}$ . Find the length that the ladder now has to be extended to.

[3]

Question 7

SLPaper 2

A hiker runs 620 m in the direction $226^{\circ}$ to a checkpoint, and then 360 m in the direction $136^{\circ}$ to the finish. To find :

Direct distance from the starting point to the finishing point.

[3]

Bearing of the finishing point from the starting point.

[1]

Question 8

SLPaper 2

Nile stands 15 m above the ground on the third floor balcony of a hotel and can see Max in the park. The angle of elevation from Max to Nile is $31^{\circ}$ .

Find the distance between Max and Nile.

[2]

Lucy is standing on the other side of the park. The distance between Lucy and Nile is 2.5 times the distance between Max and Nile. Calculate the angle of depression from Nile to Lucy.

[3]

Question 9

SLPaper 2

To find $\theta$ in the figure. [Answer in degree]
To find the length of AB in the figure. [Answer in m ]

To find $\theta$ in the figure. [Answer in degree]

[4]

To find the length of AB in the figure. [Answer in m ]

[3]

Question 10

SLPaper 2

A gymnast is competing in the event. Two bars A and B are placed in the vertical order as shown in the figure. It can be assumed that the gymnast is traveling in a straight line when moves from points A to B .

To find the distance between the points A and B .

[2]

To find the angle of depression from point A to point B .

[3]

When the gymnast is hanging vertically from the higher bar with her arms fully extended, there is a distance of 0.5 m between point A and her eye level. To find the difference between the angle of depression calculated in part 2. and the angle of depression that the gymnast sees to point B .

[3]

SL 3.3—Angles of elevation and depression, bearings Questionbank