Download Name: Date: The Sine Ratio i) Complete the table below using the

Name: _______________________
Date: __________________
The Sine Ratio
i)
Complete the table below using the triangles on the next page.
Side Opposite 
Name
Measure
ABC
DEF
GHJ
KLM
PON
Hypotenuse
Name
Measure
Ratio
opp/hyp
Ratio
3 decimals
A
D
F

B
C

E
G
L

H
J
P
K
N


O
M
ii)
If the measure of one angle of a right-angled triangle is kept constant, then what can
you conclude about the following ratio:
length of side opposite angle
length of hypotenuse
Sine  = length of side opposite angle
length of hypotenuse
or more commonly, sin  = opp
hyp
To find the ratio of opp:hyp, given the angle, use your calculator; i.e., sin 40  0.6428
Important Note: Ensure your calculator is in “degree” or “deg” mode.
Determine the ratios for the following angles:
a)
sin 30 =
b)
sin 130 =
c)
d)
sin 289 =
sin 195 =
To find the angle, given the ratio, use your calculator by pressing 2nd function key before the
sin key; i.e., if sin  = 0.6428, then to determine  press 2nd sin 0.6428  40.
Determine the angle for the following ratios:
a)
sin  = 0.7431
b)
sin A = 0.5299
c)
d)
sin C = -0.9962
sin B = -0.2588
Solving Problems Using the Sine Ratio
Remember: sin  
opp
adj
To solve problems using the sin ratio, you must know:
i)  an angle and either the opposite or hypotenuse side length to find the hypotenuse or
opposite side, or
ii)
the opposite and hypotenuse side lengths to find the angle.
Example:
Jack places a 12m ladder on level ground and leans it on a vertical wall so that the ladder
makes a 70 angle with the ground. How far up the wall does the ladder reach?
Solution:
Let x represent the distance up the wall in metres.
sin 70 =
x
12
x = 12 sin 70
x 12(0.9397)
12 m
x
x  11.3
 The ladder reaches 11.3 m up the wall.
70
Problems
1.
a)
Determine the unknown quantity for each of the following right triangles (round to one
decimal place).
b)
x
12 cm
x
11 cm
60
40
c)
4 cm
15 cm

2.
A support cable 60 m long connects the top of a pole to the ground. The cable makes an
angle of 72 with the ground. Calculate the height of the pole. Include a diagram with
your solution.
3.
A tree known to be 50 m high casts a shadow that is 17 m long. What angle do the sun’s
rays make with the ground at this time of day? Include a diagram with your solution.
4.
The angle of elevation of the top of a building is 72 from a point 60.0 m from the foot
of the building. Find the height of the building. Include a diagram with your solution.
5.
Find the height of a tree that casts a shadow 25.9 m long when the angle of elevation
of the sun is 41. Include a diagram with your solution.
6.
What angle will a 73 m guy wire make with the ground if it secures a tower from a point
45 m up the tower? Include a diagram with your solution.