Trigonometric Ratios Worksheet Page 18
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2210. Sheila is standing at point A west of a
13. Michael is an architect who has designed
mountain in the Kootenay region of
a cottage with a roof that has two sides
British Columbia. From point A, the
with different slopes. The shorter side of
angle of elevation of the top of the
the roof is 12 ft in length and makes an
mountain is 38°. From point B, which
angle of 68° with the top of the building.
is 10 560 ft to the east of point A, the
The longer side of the roof makes an
angle of elevation of the top of the same
angle of 28° with the top of the building.
mountain is 42°. Determine the height of
a) Draw a diagram to represent this
the mountain.
situation.
C
b) Determine the length of the other
side of the roof.
h
C
14. A rocket, launched vertically from
38°
42°
A
B
point C, is tracked by two tracking stations
D
at A and B. Data from the launch were
11. A triangular delta has been formed at
recorded according to the diagram below.
the mouth of a large river by sediment
D
deposits. The distance from the coast to
the starting point of the delta is 80 km,
and the angles formed by the coastline
and two sides of the triangular delta are
58° and 47°. Determine the length of the
delta along the coastline.
coast
x
58°
47°
42.5°
C
42.6°
30°
A
25.2°
80 km
300 m
B
a) Determine the height, h, of the rocket
as calculated from tracking station A.
12. A triangular deck is to be added to the
back wall of a house. The length of the
b) Determine the height, h, of the rocket
side of the deck that will be attached
as calculated from tracking station B.
to the house is 20 ft, and the other two
c) Are the approximate results for the
sides form angles of 32° and 65° with
calculated heights of the rocket the same
the side that is attached to the wall of
or different for parts a) and b)? Explain.
the house.
a) Draw a diagram to represent this
15. Two boats, A and B, are in a harbour
situation.
close to a marina at point C. Boat A is
38 ft from the marina. The angle between
b) Determine the length of the shortest
AC and BC is 51°, and the angle between
side of the deck.
AC and AB is 65°. From boat A, the angle
of depression to the anchor directly below
boat B is 50°. Determine the distance
from boat A to the anchor directly below
boat B.
18 MHR • Chapter 1 978-0-07-090893-2
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