3.3 Applications of trigonometry questions for IB Maths AA

29 questions on Applications of trigonometry, written by Augment in the style of IB exam papers. Six of them are below in full, to answer on paper.

IB Mathematics: Analysis and Approaches
Part of 3 Geometry and trigonometry
SL and HL

Questions by paper and level

SL and HL questions are for students at either level. HL only questions cover what only HL students study.

Paper	SL and HL	HL only	All
Paper 1	7	0	7
Paper 2	15	7	22
Every paper	22	7	29

Counted on 10 November 2026

Questions to try

Written by Augment in the style of IB exams, not past papers. Answer them on paper, then check each one against its markscheme with a free account.

Question 1 · AA-00098Paper 1 · 6 marks

A vertical cliff [FT] has its foot F on horizontal ground and its top T at a height of $h$ metres above F. The points A and B lie on the ground on a straight line through F, with B between A and F, and $A B = 40$ m.

The angle of elevation of T from A is $30^{\circ}$ and the angle of elevation of T from B is $60^{\circ}$ .

(a)
Find $A \hat{T} B$ .
2 marks
(b)
Hence, show that $B T = 40$ m.
2 marks
(c)
Find the exact value of $h$ .
2 marks

The markschemeCheck this one with a free account

Question 2 · AA-00089Paper 2 · 15 marks

A farmer owns a field in the shape of a quadrilateral $A B C D$ . The diagonal $[A C]$ divides the field into two triangles. $A B = 85$ m, $B C = 110$ m and $A \hat{B} C = 104 °$ .

(a)
Find $A C$ .
3 marks
(b)
Find $B \hat{A} C$ .
3 marks
(c)
It is also known that $C D = 70$ m and $A \hat{C} D = 57 °$ . Find $A D$ .
3 marks
(d)
Find the area of the field.
4 marks
(e)
The farmer puts a fence around the boundary of the field. The fence costs $14.50 per metre. Find the cost of the fence, correct to the nearest dollar.
2 marks

The markschemeCheck this one with a free account

Question 3 · AA-00102Paper 1 · 6 marks

A vertical pole [PT] stands on horizontal ground, with its base at P. A straight wire joins the top of the pole, T, to a point A on the ground, where $P A = 6$ m. The wire makes an angle of $60^{\circ}$ with the ground.

(a)
Find the length of the wire [TA].
2 marks
(b)
Find the exact height of the pole.
2 marks
(c)
A second straight wire joins T to a point B on the ground, so that P lies on [AB]. This wire makes an angle of $45^{\circ}$ with the ground.
Find the exact distance AB.
2 marks

The markschemeCheck this one with a free account

Question 4 · AA-00096Paper 2 · 15 marks

The end wall of a house is in the shape of a triangle $A B C$ on top of a rectangle. The horizontal base of the triangle is $[A B]$ , with $A B = 9.6$ m. The two sloping edges of the roof are $[A C]$ and $[B C]$ , with $C \hat{A} B = 35 °$ and $C \hat{B} A = 50 °$ .

(a)
Write down the size of $A \hat{C} B$ .
1 mark
(b)
Find $A C$ .
3 marks
(c)
Find the height of $C$ above $[A B]$ .
2 marks
(d)
Find the area of triangle $A B C$ .
2 marks
(e)
A straight support beam joins $A$ to the point $N$ on $[B C]$ , where $B N = 2$ m. Find the length of the beam.
3 marks
(f)
Find the angle between the beam and the horizontal.
2 marks
(g)
The roof is made of two rectangles of length $12$ m, with widths $A C$ and $B C$ . Find the total area of the roof.
2 marks

The markschemeCheck this one with a free account

Question 5 · AA-00106Paper 1 · 6 marks

A boat crosses a lake. It sails 5 km from point A to point B on a bearing of $030^{\circ}$ , then 3 km from point B to point C on a bearing of $090^{\circ}$ .

(a)
Show that $A \hat{B} C = 120^{\circ}$ .
2 marks
(b)
Find the distance AC.
2 marks
(c)
Find the exact area of triangle ABC.
2 marks

The markschemeCheck this one with a free account

Question 6 · AA-00097Paper 2 · 6 marks

Mira is flying a kite on level ground. She holds the end of the string 1.2 m above the ground. The string is straight, has length 85 m, and makes an angle of $52^{\circ}$ with the horizontal.

(a)
Find the height of the kite above the ground.
2 marks
(b)
The wind drops. The length of the string does not change, but it now makes an angle of $38^{\circ}$ with the horizontal.
Find how far the kite has descended.
2 marks
(c)
Find the horizontal distance between Mira and the point on the ground directly below the kite when the string makes an angle of $38^{\circ}$ with the horizontal.
2 marks

The markschemeCheck this one with a free account

Practice all 29 in Augment

Free with an account. Every question has its markscheme, and Augment keeps the ones you got wrong so you can come back to them.

Start free Log in

The notes on 3.3 Applications of trigonometry

Check your answers in Augment

A free account opens all 29 questions on Applications of trigonometry with their markschemes, and keeps a record of what you have marked.

Start free

Questions by paper and level

Questions to try

Practice all 29 in Augment

More questions in Geometry and trigonometry

Check your answers in Augment