IB Maths AI SL · Unit 3: Geometry and Trigonometry
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 the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
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 →
The question bank covers these right-angled trigonometry question types (number of questions in brackets):
A $6.5\text{ m}$ ladder leans at $72^\circ$. Find the horizontal distance from wall to foot.
1. Ratio: $\cos 72^\circ = \frac{x}{6.5}$.
2. Solve: $x = 6.5\cos 72^\circ = 2.0086\ldots$
3. State: $\mathbf{2.01\text{ m}}$.
Right triangle: base $14$, height $9$. Find the angle of elevation.
1. Ratio: $\tan\theta = \frac{9}{14}$.
2. Inverse: $\theta = \tan^{-1}(9/14)$.
3. State: $\mathbf{32.7^\circ}$.
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: $\mathbf{h = 37.9\text{ m}}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
A vertical building is \(15 \text{ m}\) tall. At a certain time of day, it casts a horizontal shadow of exactly \(20 \text{ m}\) on the ground.
Calculate the angle of elevation of the sun.
A lighthouse is \(45 \text{ m}\) 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.
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.
All 11 right-angled trigonometry questions with mark schemes →
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).
Both. In the bank, Paper 1: 4 · Paper 2: 7. Practise with your GDC — AI papers expect calculator methods throughout.
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.