Bearings & SSA: Ambiguous Case (Trignometric Concepts)

1) A ship sails 40 km on a bearing of 030°. From that point, the angle between its course and a line to a harbor is 45°. The distance to the harbor could have two possible values. Which law is best used?

Law of Cosines

Pythagorean Theorem

Law of Sines

Special Right Triangles

2) When solving SSA triangles with the Law of Sines, which situation can create the ambiguous case?

One side and two angles are known

Two sides and the included angle are known

Two sides and a non-included angle are known

All three sides are known

3) A plane flies 120 km on a bearing of 045°. From its position, the angle between its course and a lighthouse is 35°. Using the Law of Sines, which unknown is typically found first?

The second angle

The third angle

The distance to the lighthouse

The altitude

4) In navigation, if an SSA setup produces an angle larger than 90° that doesn’t fit the triangle, what is the conclusion?

Two possible triangles exist

No triangle exists

Only one obtuse triangle exists

It’s a right triangle

5) A ship travels 60 km east. The angle from its course to a harbor is 40°. Which law should be used to find the harbor’s distance?

Law of Cosines

Law of Sines

Pythagorean Theorem

Special Right Triangles

6) Which condition guarantees only one unique triangle with SSA?

Opposite side is shorter than altitude

Opposite side is equal to altitude

Opposite side is greater than adjacent side

Opposite side is less than adjacent side

7) A plane flies 80 km north. A lighthouse is observed at a 50° angle from its course. Which law is applied?

Law of Cosines

Law of Sines

Special Right Triangles

Pythagorean Theorem

8) If SSA gives two possible triangles, what is true about the sine of the angle?

Sin θ > 1

Sin θ < 0

Sin θ corresponds to two possible angles

Sin θ = 0

9) A boat sails 100 km northeast. The angle from its path to an island is 60°. What is solved first with the Law of Sines?

Distance to island

First angle

Third angle

Bearing angle

10) Which situation does not create ambiguity?

SSA with opposite side shorter than altitude

SSA with opposite side longer than adjacent side

SSA with opposite side shorter than adjacent side but greater than altitude

SSA with opposite side exactly equal to altitude

11) A pilot knows two sides of a triangle and the angle opposite one of them. Which law is best?

Law of Cosines

Law of Sines

Pythagorean Theorem

Special Right Triangles

12) In SSA, when the given angle is acute and the opposite side is shorter than the altitude, what happens?

Two triangles exist

No triangle exists

Exactly one right triangle exists

An obtuse triangle exists

13) A triangle with SSA information produces sin θ = 0.8. What are the two possible angles?

53.1° and 126.9°

36.9° and 143.1°

45° and 135°

60° and 120°

14) A ship sails 90 km on a bearing of 030°. A lighthouse is seen at a 40° angle. Which law should be used?

Pythagorean Theorem

Law of Cosines

Law of Sines

Special Right Triangles

15) Which of these is always a case of SSA ambiguity?

Side–angle–side (SAS)

Side–side–angle (SSA)

Angle–side–angle (ASA)

Side–side–side (SSS)

16) If SSA produces an angle whose sine is greater than 1, what does it mean?

Two triangles exist

One triangle exists

No triangle exists

Triangle is right

17) A boat travels 70 km. The angle from its course to a harbor is 50°. Distance to harbor is found with:

Law of Cosines

Law of Sines

Pythagorean Theorem

Special Right Triangles

18) Which situation can produce exactly one right triangle under SSA?

Opposite side equals altitude

Opposite side > adjacent side

Opposite side < altitude

Opposite side slightly > altitude

19) A plane knows two sides and a non-included angle. Which law is used?

Law of Cosines

Pythagorean Theorem

Law of Sines

Special Right Triangles

20) If SSA produces an obtuse angle and the given angle is acute, what happens?

Two possible triangles exist

No triangle exists

Only one obtuse triangle exists

Triangle is isosceles

Bearings and Ambiguous Cases (SSA Triangles)

1) A ship sails 40 km on a bearing of 030°. From that point, the angle between its course and a line to a harbor is 45°. The distance to the harbor could have two possible values. Which law is best used?

2)

What first name or nickname would you like us to use?

2) When solving SSA triangles with the Law of Sines, which situation can create the ambiguous case?

3) A plane flies 120 km on a bearing of 045°. From its position, the angle between its course and a lighthouse is 35°. Using the Law of Sines, which unknown is typically found first?

4) In navigation, if an SSA setup produces an angle larger than 90° that doesn’t fit the triangle, what is the conclusion?

5) A ship travels 60 km east. The angle from its course to a harbor is 40°. Which law should be used to find the harbor’s distance?

6) Which condition guarantees only one unique triangle with SSA?

7) A plane flies 80 km north. A lighthouse is observed at a 50° angle from its course. Which law is applied?

8) If SSA gives two possible triangles, what is true about the sine of the angle?

9) A boat sails 100 km northeast. The angle from its path to an island is 60°. What is solved first with the Law of Sines?

10) Which situation does not create ambiguity?

11) A pilot knows two sides of a triangle and the angle opposite one of them. Which law is best?

12) In SSA, when the given angle is acute and the opposite side is shorter than the altitude, what happens?

13) A triangle with SSA information produces sin θ = 0.8. What are the two possible angles?

14) A ship sails 90 km on a bearing of 030°. A lighthouse is seen at a 40° angle. Which law should be used?

15) Which of these is always a case of SSA ambiguity?

16) If SSA produces an angle whose sine is greater than 1, what does it mean?

17) A boat travels 70 km. The angle from its course to a harbor is 50°. Distance to harbor is found with:

18) Which situation can produce exactly one right triangle under SSA?

19) A plane knows two sides and a non-included angle. Which law is used?

20) If SSA produces an obtuse angle and the given angle is acute, what happens?