WARM-UP
Sine Law: The Ambiguous Case
1. A lighthouse at point L is 10 km from a yacht at point Y and 8 km from a sailboat at point B.
From the yacht, the lighthouse and the sailboat are separated by an angle of 48 o.
a) Is it necessary to consider the ambiguous case? Explain.
b) Sketch possible diagrams for this situation.
c) Determine the distance from the yacht to the sailboat, to the nearest tenth of a kilometre.
[9.7 km, 3.7 km]
2. During a canoe trip, Sam stops at a point along the south side of the river that flows from east
to west. From here he can see a forest lookout tower located 2.5 km away at a point on the
north side of the river. As Sam continues his trip, he stops at another point on the south side
of the river that is 1.8 km from the tower. The angle between the tower, Sam’s first stop and
his second stop is 35o.
a) Is it necessary to consider the ambiguous case? Explain.
b) Sketch possible diagrams for this situation.
c) Determine the distance between Sam’s first and second stops. [3.14 km, 0.96 km]
WARM-UP
Sine Law: The Ambiguous Case
1. A lighthouse at point L is 10 km from a yacht at point Y and 8 km from a sailboat at point B.
From the yacht, the lighthouse and the sailboat are separated by an angle of 48 o.
d) Is it necessary to consider the ambiguous case? Explain.
e) Sketch possible diagrams for this situation.
f) Determine the distance from the yacht to the sailboat, to the nearest tenth of a kilometre.
[9.7 km, 3.7 km]
2. During a canoe trip, Sam stops at a point along the south side of the river that flows from east
to west. From here he can see a forest lookout tower located 2.5 km away at a point on the
north side of the river. As Sam continues his trip, he stops at another point on the south side
of the river that is 1.8 km from the tower. The angle between the tower, Sam’s first stop and
his second stop is 35o.
d) Is it necessary to consider the ambiguous case? Explain.
e) Sketch possible diagrams for this situation.
f) Determine the distance between Sam’s first and second stops. [3.14 km, 0.96 km]
WARM-UP
Sine Law: The Ambiguous Case
1. A lighthouse at point L is 10 km from a yacht at point Y and 8 km from a sailboat at point B.
From the yacht, the lighthouse and the sailboat are separated by an angle of 48 o.
g) Is it necessary to consider the ambiguous case? Explain.
h) Sketch possible diagrams for this situation.
i) Determine the distance from the yacht to the sailboat, to the nearest tenth of a kilometre.
[9.7 km, 3.7 km]
2. During a canoe trip, Sam stops at a point along the south side of the river that flows from east
to west. From here he can see a forest lookout tower located 2.5 km away at a point on the
north side of the river. As Sam continues his trip, he stops at another point on the south side
of the river that is 1.8 km from the tower. The angle between the tower, Sam’s first stop and
his second stop is 35o.
g) Is it necessary to consider the ambiguous case? Explain.
h) Sketch possible diagrams for this situation.
i) Determine the distance between Sam’s first and second stops. [3.14 km, 0.96 km]