IB Triangle Trig Questions
1. A triangle has sides of length 4, 5, 7 units. Find, to the nearest tenth of a degree, the size of the largest
angle.
2. The diagram shows a vertical pole PQ, which is supported by two wires fixed to the horizontal ground
at A and B.
P
36 B
30
Q
BQ = 40 m
P B̂ Q = 36°
B Â Q = 70°
A B̂ Q = 30°
70
A
Find
(a)
the height of the pole, PQ;
(b)
the distance between A and B.
3. Town A is 48 km from town B and 32 km from town C as shown in the diagram.
C
32km
A
48km
B
Given that town B is 56 km from town C, find the size of angle CÂB to the nearest degree.
4. The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.
5
7
8
Find
(a) the size of the smallest angle, in degrees;
(b)
the area of the triangle.
diagram not to scale
IB Triangle Trig Questions
5. The diagrams below show two triangles both satisfying the conditions
AB = 20 cm, AC = 17 cm, AB̂C = 50°.
diagrams not to scale
Triangle 1
Triangle 2
A
A
B
C
(a)
Calculate the size of AĈB in Triangle 2.
(b)
Calculate the area of Triangle 1.
B
C
6. Two boats A and B start moving from the same point P. Boat A moves in a straight line at 20 km h–1
and boat B moves in a straight line at 32 km h–1. The angle between their paths is 70°. Find the
distance between the boats after 2.5 hours.
7. In triangle ABC, AC = 5, BC = 7, Â = 48°, as shown in the diagram.
C
5
A
48°
7
diagram not to scale
B
Find B̂, giving your answer correct to the nearest degree.
IB Triangle Trig Questions
8. The points P, Q, R are three markers on level ground, joined by straight paths PQ, QR, PR as shown in
the diagram. QR = 9km, PQ̂R = 35°, PR̂Q = 25°.
P
Q
(a)
35°
25°
9 km
R
Find the length PR.
(b) Tom sets out to walk from Q to P at a steady speed of 8 km h–1. At the same time, Alan sets
out to jog from R to P at a steady speed of a km h–1. They reach P at the same time. Calculate
the value of a.
9. The graph of the function f(x) = 3x – 4 intersects the x-axis at A and the y-axis at B.
(a) Find the coordinates of
(i) A;
(ii)
(c)
B.
Let O denote the origin. Find the area of triangle OAB.
10. The following diagram shows a triangle ABC, where BC = 5 cm, B̂ = 60°, Ĉ = 40°.
A
B
(a)
Calculate AB.
(b)
Find the area of the triangle.
40°
60°
5 cm
C
IB Triangle Trig Questions
11. The diagram shows a triangular region formed by a hedge [AB], a part of a river bank [AC] and a
fence [BC]. The hedge is 17 m long and BÂC is 29°. The end of the fence, point C, can be positioned
anywhere along the river bank.
(a) Given that point C is 15 m from A, find the length of the fence [BC].
15 m
A
river bank
C
29°
17 m
B
(b)
The farmer has another, longer fence. It is possible for him to enclose two different triangular
regions with this fence. He places the fence so that AB̂C is 85°.
(i) Find the distance from A to C.
(ii)
Find the area of the region ABC with the fence in this position.