Elevation from $A$ is $35^\circ$. From $B$, $20\text{ m}$ closer, it is $48^\circ$. Find the tower height.

1. Two equations : $\tan 48^\circ = \frac{h}{x}$, $\tan 35^\circ = \frac{h}{x+20}$. 2. Eliminate $x$ : $x = \frac{h}{\tan 48^\circ}$. 3. Substitute and solve on GDC. 4. State : $\mathbf{h = 37.9\text{ m}}$.

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IB Maths AI SL · Unit 3: Geometry and Trigonometry

IB Maths AI SL Right-Angled Trigonometry Questions

Updated October 2026

Exam-style IB Maths AI SL right-angled trigonometry questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step, showing the working that earns the marks — then try the practice questions and check your working against the mark scheme.

11 questions
Paper 1: 4
Paper 2: 7
6 easy
4 medium
1 hard
3 worked examples

Practise Right-Angled Trigonometry questions →

What you need to know

The single most common confusion in SL AI Paper 1. Sine rule when you have a matching angle-side pair; cosine rule when you have two sides + included angle. Practise until it's automatic. Sine rule vs cosine rule — the decision tree overview →

Standing at the top of a cliff looking down at a boat, or standing at the base of a tower looking up. SL AI always asks for BOTH the horizontal distance and the vertical height. 3D trigonometry — angle of elevation and depression overview →

What's examined in AI SL right-angled trigonometry

The question bank covers these right-angled trigonometry question types (number of questions in brackets):

Angles of Elevation & Depression (5)
Fundamental Ratios & Pythagoras (4)
Composite Problems & Bearings (2)

Key formulas

Cosine rule: $c^{2} = a^{2} + b^{2} - 2 a b \cos C$
Right-angled triangle (SOHCAHTOA): $\sin θ = \frac{O}{H}, \cos θ = \frac{A}{H}, \tan θ = \frac{O}{A}$
Sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

In the same notation as the IB formula booklet. All AI SL formulas →

Explained, with a worked example: Pythagoras' theorem · SOH CAH TOA

Where students lose marks on right-angled trigonometry

Examiner's noteTriangles and 3D: wrong rule, wrong angle, missing units

Where marks are lost: Candidates assumed a right angle that was not there (or used the sine rule in a right-angled triangle), found an angle other than the one named, used the wrong radius or only one of two areas, missed an arc length in a curved surface, forgot units where they were required, and did not give an answer in standard form when asked. Drawing a diagram helped.

Examiners flagged this in 3 exam series (May 2024, November 2024, November 2025). Summarised in our own words from IB subject reports, IB Programme Resource Centre. Read the full note →

Right-Angled Trigonometry worked examples

Worked example 1: SOH-CAH-TOA — side length · easy

A $6.5 m$ ladder leans at $72^{\circ}$ . Find the horizontal distance from wall to foot.

Solution

3 steps

Examiner tip: To 3 s.f.,

2.01

keeps the zeros. Writing

2.0

loses a mark.

Worked example 2: Angle of elevation · medium

Right triangle: base $14$ , height $9$ . Find the angle of elevation.

Solution

3 steps

Examiner tip: Elevation = UP from horizontal; depression = DOWN.

Worked example 3: Chained triangles — tower height · hard

Elevation from $A$ is $35^{\circ}$ . From $B$ , $20 m$ closer, it is $48^{\circ}$ . Find the tower height.

Solution

4 steps · 1 to fill in

Examiner tip: Two overlapping right-triangles: two equations, eliminate the horizontal, solve on GDC.

Try these IB Maths AI SL right-angled trigonometry questions

Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.

Question 1 · easy · 3 marks · Paper 2

A vertical building is $15 m$ tall. At a certain time of day, it casts a horizontal shadow of exactly $20 m$ on the ground.

Calculate the angle of elevation of the sun.

Attempt it and see the mark scheme →

Question 2 · medium · 4 marks · Paper 2

A lighthouse is $45 m$ tall. From the top of the lighthouse, the angle of depression to a boat at sea is $15^{\circ}$ .

Assuming the base of the lighthouse is at sea level, calculate the horizontal distance from the base of the lighthouse to the boat.

Full worked solution Free, no sign-in

The angle of elevation from the boat to the top of the lighthouse equals the angle of depression, $15^{\circ}$ (alternate angles). (M1)
Use tangent in the right-angled triangle: $\tan (15^{\circ}) = \frac{45}{d}$ M1
Rearrange: $d = \frac{45}{\tan (15^{\circ})}$ (A1)
$d = 167.94 \dots \approx 168 m$ A1

Every question here has a full worked solution. See them all →

Question 3 · hard · 5 marks · Paper 2

Two observers, A and B, are standing on horizontal ground on the same side of a vertical tower. The distance between observer A and observer B is $50$ m. From observer A, the angle of elevation to the top of the tower is $30^{\circ}$ . From observer B, who is closer to the tower, the angle of elevation is $45^{\circ}$ .

Calculate the exact height of the tower.

Attempt it and see the mark scheme →

Free account — sign in to download Topic PDF: 7 questions with worked answers · 4 pages · 144 KB

All 11 right-angled trigonometry questions with mark schemes →

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Revise right-angled trigonometry for the exam

FAQ

How many IB Maths AI SL right-angled trigonometry questions are there?

There are 11 exam-style right-angled trigonometry questions in the AI SL question bank (Paper 1: 4 · Paper 2: 7), graded 6 easy, 4 medium, 1 hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is right-angled trigonometry on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 4 · Paper 2: 7. Practise with your GDC — AI papers expect calculator methods throughout.

Where can I get the mark schemes?

Open the AI SL Unit 3 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

What else is free here

Save your answers and track your progressA free account remembers the questions you have done on every topic and brings you back to this page.

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IB Maths AI SL Right-Angled Trigonometry Questions

Try it first

What you need to know

What's examined in AI SL right-angled trigonometry

Key formulas

Where students lose marks on right-angled trigonometry

Right-Angled Trigonometry worked examples

Worked example 1: SOH-CAH-TOA — side length · easy

Solution

Worked example 2: Angle of elevation · medium

Solution

Worked example 3: Chained triangles — tower height · hard

Solution

Try these IB Maths AI SL right-angled trigonometry questions

Question 1 · easy · 3 marks · Paper 2

Question 2 · medium · 4 marks · Paper 2

Full worked solution Free, no sign-in

Question 3 · hard · 5 marks · Paper 2

Revise right-angled trigonometry for the exam

FAQ

What else is free here

More AI SL Unit 3 topics