Download Applications of trigonometry

‫مدرسة درويش بن كرم‬
Darweesh Ben karam school
Abu Dhabi
‫أبوظبي‬
Applications of trigonometry
Name: ___________________________
Section A Multiple Choice
1
The length x is closest to:
A
B
C
D
2
4
5.14
6.13
9.53
10.44
The length of the side marked x is
closest to:
A 11 m
B 14 m
C 17 m
D 21 m
The value of the angle marked  is
closest to:
5
A
B
C
D
3
37°
39°
52°
53°
A compass bearing of S50°W is
equivalent to a true bearing of:
A
B
C
D
130°
150°
230°
250°
The size of angle marked  to the
nearest degree is:
A
B
C
D
21°
35°
44°
46°
6
The size of angle marked  can be
found using which of the following
expressions?
A
B
C
D
7
8.03 square units
9.64 square units
11.49 square units
15.00 square units
Town B is 8 km directly north of town
A, and town C is 10 km on a bearing of
120°T from A. The distance of town B
from town C is:
A
B
C
D
9.17 km
12.81 km
15.62 km
17.39 km
In the figure drawn below the value of x
can be found using which of the
following expressions?
A
B
C
D
sin  =
The area of the triangle correct to 2
decimal places is:
A
B
C
D
8
8 sin 50
15
15 sin 50
sin  =
8
50 sin 15
sin  =
8
8 sin 15
sin  =
50
9
10
x2 = 324 cos 45°
x2 = 2754 – 2430 cos 45°
x = 45 sin 45°
None of the above
The largest angle, to the nearest degree,
is:
A
B
C
D
53°
73°
75°
77°
Applications of trigonometry Test A
Name: ___________________________
Section B Short/Extended answer
1
The angle of depression from the top of a
150 m cliff to a ship in the sea is 5°. How far is
the ship from the base of the cliff?
2
A 50 m ladder just reaches the top of a building
that is 46 m high. Calculate the angle that the
ladder makes with the horizontal, correct to the
nearest degree.
2
3
A ship sails 15 km east and then 10 km south.
Find the true bearing of the ship from its
starting point, correct to the nearest degree.
2
4
A helicopter flies 30 km in a direction of
N47°E. How far east of the starting point is it,
correct to 2 decimal places?
2
5
In the figure below, use the sine rule to find the
length of the side marked x, correct to 1
decimal place.
6
From point A, due west of the foot of a
building, the angle of elevation to the top of the
building T is 50°. From point B, due east of the
building, the angle of elevation to the top of the
building is 35° as shown below. The distance
between A and B is 60 m.
(a) Find the size of ATB.
(b) Show that AT can be given by the
60 sin 35
expression: AT =
sin 95
(c) Find the height (h) of the building correct to
1 decimal place.
7
In triangle ABC, a = 17 m, c = 15 m and
C = 54°. Find the size of angle A correct to the
nearest degree.
8
Use the cosine rule to find the length of the side
marked x in the figure below, correct to 2
decimal places.
9
Find the area of the triangle in question 8
correct to the nearest square metre.
3
10
A speed boat leaves buoy A and travels in a
direction of N60°E for a distance of 9.6 km to
reach buoy B. It then heads due north for
7.8 km to buoy C as shown below.
b2 = a2  c2  2ac cos B
b2 = 7.82 + 9.62 – 2  7.8  9.6  cos 120
 227.88
b  227.88
 15.10 km (correct to 2 decimal places)
How far is buoy C from buoy A, correct to 2
decimal places?
11
Find the smallest angle in the triangle with
sides 5 cm, 6 cm and 8 cm. Give your answer
correct to the nearest degree.
3
b2  c2  a2
2bc
2
6  82  52
cos  
268
75
cos  
96
cos   0.7813
  39°
cos  
12
The figure drawn below is a radial survey of a field.
(a) Find the size of AXB.
(b) Find the length of the boundary AB, correct to
the nearest metre.
(c) Find the area of AXB, correct to the nearest
square metre.