Trigonometric Ratios Worksheet Page 3
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229. Doug designed a sail for a model sailboat.
13. Boat A is 5 km north of a marina.
The sail is in the shape of a right triangle.
Boat B is 5 km east of the marina.
a) D etermine the distance between the
two boats.
b) D escribe an alternative method that
can be used to solve this problem.
12 cm
h
14. A patio in the shape of a regular hexagon
has side lengths 4 m. Determine the area
of the patio.
60°
15. ��e �e��n�����
��e �e��n����� Use geometry software
w
to construct a circle with radius 1 unit.
Construct point A on the circle in
quadrant I. Construct a segment joining
A to the origin, O, to form angle
a) Determine the height, h, of the sail.
in standard position. Determine the
b) Determine the width, w, of the sail.
coordinates of A.
a) C alculate the sine, cosine, and
10. Alicia is on an overnight camping trip. At
tangent ratios of ∠, using x and y.
the front of her tent, the distance from
b) D rag point A around the circle. What
the top of the tent to the ground on either
do you notice?
side is 8 ft.
16. Determine the exact value of
cos 30° × sin 240° + sin 330°.
8 ft
8 ft
C
17. Determine all the possible measures of ,
45°
45°
where 0° ≤ ≤ 360°.
__
a) Determine the height of Alicia’s tent.
√
3
1
___
__
a) cos =
b) sin =
2
2
b) Determine the width of the floor of
her tent.
18. Determine h.
11. A 3-m long brace is placed against a wall
D
so the bottom of the brace makes an
angle of 60° with the ground.
h
a) Draw a diagram to represent this
situation.
60°
30°
b) How far up the wall is the top of the
C
B
16 m
A
brace?
y
x
__
__
r , show
19. Given sin =
r and cos =
12. A 4-m long ramp is placed against a wall.
sin
_____
cos =tan .
that
The ramp makes an angle of 30° with
the ground. How far from the wall is the
y
x
__
__
r , and
20. Given sin =
r , cos =
bottom of the ramp?
2
2
2
2
2
x
+ y
= r
, show that sin
+ cos
= 1.
978-0-07-090893-2 Mathematics for College Technology 12 Study Guide and Exercise Book • MHR 3
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