Download Worksheet 4.2

Maths Quest 11 Maths B for Queensland
WorkSHEET 4.2
1
Chapter 4 Triangle Trigonometry WorkSHEET 4.2
Triangle Trigonometry
Find the unknown marked sides correct to 2
decimal places.
1
Name: ___________________________
tan 37° =
10
x
4
10
tan 37
x = 1327 (correct to 2 decimal places)
10
sin 37° =
h
10
h =
sin 37
h = 16.62 (correct to 2 decimal places)
x=
2
Find the value of  .
10
8
tan   1.25
tan  
2
   51.3
3
From a vertical fire tower 50 m high, the angle
of depression is 4° to a fire. How far away is
the fire to the nearest metre is the fire?
3
tan 4  
h 
50
d
50
tan 4 
h  715 m (to the nearest metre)
Maths Quest 11 Maths B for Queensland
4
Chapter 4 Triangle Trigonometry WorkSHEET 4.2
A person 1.6 m tall stands 30 m from a building
and measures the angle of elevation to the top
of the building as 48°. How high is the building
to the nearest metre?
2
3
h
30
 h = 30  tan 48°
h = 333 m
Height of building = 33.3  1.6 m
= 34.9
= 35 m (to the nearest metre)
tan 48° =
5
In triangle ABC, a = 8, c = 12, and C = 52°.
Find A.
3
sin A sin 52 

8
12
8  sin 52 
12
sin A  0.5253
sin A 
A  31.7 
6
Find the value of length x correct to 1 decimal
place.
x
sin 57 

x 
8
sin 62 
8  sin 57 
sin 62 
x  7.6 (correct t o 1 decimal place)
3
Maths Quest 11 Maths B for Queensland
7
Chapter 4 Triangle Trigonometry WorkSHEET 4.2
Consider the figure drawn below.
(a)
ADB  40 
a
b

sin A sin B
BD
50

sin 20  sin 40 
BD 
(a)
Find an expression for the length BD.
(b)
Find h correct to 1 decimal place.
(b)
3
50 sin 20 
sin 40 
opp
hyp
h
sin 60  
BD
sin  
h  BD sin 60 

50 sin 20  sin 60 
sin 40 
 23.0
8
Find the third side of the triangle ABC, given
a = 8, c = 12 and B = 75°. State your answer
correct to 2 decimal places.
9
Find the smallest angle in the triangle with
sides 5, 8 and 10.
b2 = 82  122  (2  8  12  cos 75°)
= 64  144  49.69
= 158.31
b = 158.31
= 12.58 (correct to 2 decimal places)
3
8 2  10 2  5 2
2  8  10
139
cos  
160
cos   0.8688
3
cos  
   29.7 
Maths Quest 11 Maths B for Queensland
10
Chapter 4 Triangle Trigonometry WorkSHEET 4.2
A triangle has sides 6 cm, 7 cm and 9 cm. Find
the size of the largest angle correct to the
nearest minute.
Largest side lies opposite the largest angle.
b2  c2  a2
cos A 
2bc
cos  


 
62  72  92
267
36  49  81
84
4
84
 4
cos 1  
 84 
 87 16
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