Download MTH-4103-1 D - WordPress.com

ANSWER KEY
MTH-4103-1 D
Trigonometry I
1. Find the trigonometric ratios of the following:
a) CosA = b/c
d) CosB = a/c
b) TanB = b/a
e) TanA = a/b
A
C
b
a
c
B
c) SinA = a/c
/5
2. Triangle XYZ is right-angled in Y. Which of the following trigonometric
functions have the same value?
CosZ
SinZ
SinX
TanZ
CosX
TanX
/4
3. Given the triangle:
E
33 cm
D
F
42 cm
a) Calculate the measure of angle E to the nearest degree.
E = 51.842°
E = tan-1(42/33)
81 cm
22°
b) Calculate the length of the hypotenuse to the nearest tenth.
Sin(22°) = 81/x
x = 216.22 cm
/5
4. Given the triangle below, find m AB .
3.6 ÷ 2 = 1.8 m
A
C = tan-1(0.7/1.8) = 21.25°
3.6 m
D
?
Sin(21.25°) = x/3.6
0.7 m
C
E
B
x = 1.3 m
/5
5. Given the triangle below, find the measure of the side RT .
R
180 – 20 – 60 = 100°
32
/sin100° = x/sin60°
S
60°
20°
T
32 km
x = 28.14 km
x = 1.3 m
/10
6. Given the triangles:
E
22°
DCE = sin-1(36/55) = 40.88°
A
55 m
36 m
ACB = 180 – 90 – 40.88 = 49.11°
AE = cos(22°) = 55/x = 59.319 m
AB = tan(49.11°) = x/15 = 17.326 m
B
15 m
C
D
a) Find the measure of angle DCE to the nearest degree
40.88°
b) Find the measure of angle ACB to the nearest degree.
49.11°
c) Find m AE to the nearest tenth.
59.319 m
d) Find the measure of side AB to the nearest metre.
17.326°
/11
7. A production company is putting on “Romeo & Juliet” for the first time. In
preparation for the famous balcony scene, the set designer calculates that in order
for the ladder (3 metres long) to reach the balcony, it must form an angle of
elevation of 50°. How high is the balcony?
Sin(50°) = x/3
3m
x = 2.2981 m
?
/10
50°
8. Given the triangle below, find the measure of the side AD to the nearest tenth.
B
Tan(27°) = x/80
x = 40.762 m
(AD)2 = (50)2 – (40.762)2
50 cm
x
AD = 28.956 cm
27°
A
D
C
80 cm
/10
9. Nancy, looking at a geographic map, wanted to measure the distance between her
house and the two neighboring cities. She obtained the following results:
St-Eustache
SR
Rosemere
(SR)2 = (35)2 + (20)2 - 2∙35∙20∙Cos(40°)
(SR)2 = 1225 + 400 – 1072.46222
SR = 23.5 km
Nancy’s House
Calculate the distance between St-Eustache and Rosemere.
/10
10. Exploring the map further, Nancy discovered new information concerning the
Laurentian Autoroute and the Mille-Isle river:
Broisbriand
Lorraine
60°
Laval
Calculate the length of the bridge joining Laval to Broisbriand.
180 – 115 – 5 = 60°
22
/Sin(60°) = x/Sin(5°)
Sin(60°)x = 22(Sin(5°)
x = 22(Sin(5°)/Sin(60°)
x = 2.214 km
/10
11. From the top of a cliff, Cathy observed a ship forming a 30° angle of depression.
As the ship advances 70 metres, the angle of depression increased to 40°.
What is the height of the cliff?
10°
201.557 m
40 – 30 = 10°
90 – 40 = 50°
70
Cos(50°) = x/201.557
Sin(10°)x = 70(Sin(30°)
x = 70(Sin(30°)/Sin(10°)
x = 129.558 m
/Sin(10°) = x/Sin(30°)
x = 201.557
/10
12. A new post-modern sculpture is being erected in Central Park. Its sides measure
3 m, 7m and 9 m.
10 metres away, Anne wondered what distance separated her from the top of the
sculpture that formed a 43.5° angle of elevation.
Calculate this distance for her.
A° = Cos-1(72 + 32 – 92/2∙7∙3)
A° = Cos-1(–23/42)
A° = 123.2°
180 – 123.2 = 56.796°
x2 = (7)2 + (10)2 - 2∙7∙10∙Cos(56.796°)
x2 = 49 + 100 – 76.6666666
x = 8.5 m
/10