Ready to master bearings in trig? This free quiz is your chance to test your bearings in trigonometry skills and tackle real-world bearing problems trig with confidence. Through quick examples, you'll learn how to convert bearings to standard angle measurements and apply sin, cos, and tan for precise navigation. Whether you're reviewing angles for class or sharpening your navigation know-how, you'll face engaging trigonometry bearing questions that sharpen insight and speed. Jump in now to see how you score, then explore related challenges like our unit circle quiz or take on the plane and spherical trigonometry quiz to expand your skillset. Don't wait - dive into this trigonometry bearings quiz today and transform your approach to trig!
What bearing corresponds to due east?
090°
270°
360°
045°
Bearings are measured clockwise from north. Due east is 90° clockwise from north, which is conventionally written as 090°. This three-digit format ensures that bearings below 100° are padded with a leading zero. More on basic compass bearings can be found at Maths Is Fun.
What bearing corresponds to north-east?
045°
315°
135°
225°
North-east lies exactly halfway between north (000°) and east (090°), so its bearing is 045°. Bearings use three digits so it appears as 045°. This is standard in navigation and surveying. See Britannica: Compass Rose for more.
What bearing corresponds to south-west?
225°
135°
315°
045°
South-west is directly between south (180°) and west (270°), so the bearing is 225°. Bearings wrap around clockwise from north. The three-digit format 225° is standard. For compass basics see Maths Is Fun: Compass Directions.
The bearing of 360° corresponds to which cardinal direction?
North
East
South
West
A bearing of 360° returns to north after a full clockwise revolution. Bearings are always measured clockwise from north, so 360° coincides with 000°. Thus 360° means due north. More on this at National Geographic: Compass.
A boat sails on a bearing of 180°. Which direction is it traveling?
South
North
East
West
A bearing of 180° is measured clockwise from north and points directly south. This is the standard way to describe due south in navigation. See the concept at Wikipedia: Bearing (navigation).
The bearing of 270° corresponds to which direction?
West
East
North
South
A bearing of 270° is 270 degrees clockwise from north, which points directly west. Bearings use clockwise measurement from north as the zero reference. For more details, visit Movable Type Scripts: Bearings.
What compass direction does a bearing of 135° represent?
South-east
South-west
North-east
North-west
135° clockwise from north lands halfway between south (180°) and east (90°). That direction is south-east. Bearings are always measured from north in a clockwise sense. More equipment on directional naming is at BBC Bitesize: Compass Directions.
What bearing corresponds to north-west?
315°
045°
225°
135°
North-west is between north (000°) and west (270°) by 45°, giving 315°. Bearings are labelled clockwise from north. This three-digit notation is standard in navigation. Further reading at Maths Is Fun: Compass Rose.
Two landmarks are due east and 30° south of east from point A. What is the bearing of the second landmark?
120°
060°
150°
210°
Bearings are measured from north clockwise. South of east by 30° means starting at 90° (east) then adding 30°, giving 120°. Thus the bearing is 120°. See angle wording at Maths Is Fun: Angle Measures.
From a lighthouse, a ship is 100 m due east and another is 50 m due north of the first ship. What is the bearing of the second ship from the lighthouse (to the nearest degree)?
63°
27°
90°
117°
From the lighthouse to the second ship, ?E=100 and ?N=50. The bearing ?=arctan(?E/?N)=arctan(100/50)?63.4°, rounding to 63°. Bearings use arctan(East/North). More trigonometry details at Khan Academy: Trigonometry.
A surveyor at point A sights point B on a bearing of 070° and then turns 40° clockwise to sight point C. What is the bearing of C from A?
110°
030°
160°
100°
Starting at 070° then turning 40° clockwise yields 070+40=110°. That is the new bearing. Bearings are cumulative clockwise from north. See turning through an angle at Maths Is Fun: Angles.
A boat travels from A to B on bearing 045° for 20 km, then from B on bearing 135° for 15 km. What is its bearing from A to its final position?
82°
70°
92°
102°
Compute coordinates: B=(20 sin45,20 cos45)?(14.14,14.14), then C from B by (15 sin135,15 cos135)?(10.61,–10.61). Sum gives (24.75,3.53) so bearing=arctan(24.75/3.53)?81.8°, rounding to 82°. Details at Hotmath: Bearings.
If the bearing from P to Q is 210°, what is the reciprocal bearing from Q to P?
030°
210°
330°
150°
The reciprocal bearing is 180° different. 210°?180°=30°, so the back bearing is 030°. Bearings wrap around 360° if needed. See back bearings at BBC Bitesize.
A plane flies from point A to B on bearing 320° then to C on bearing 50°. What angle does it turn at B?
90°
40°
120°
150°
Arrival bearing at B is 320°, departure is 050°. Clockwise turn = (360?320)+50=90°. That gives the angle of turn. For more bearing-turn problems, see MathsRevision.net.
A landmark lies on a bearing of 145° from city X and another on 215° from X. What is the acute angle between the directions to the two landmarks?
70°
90°
120°
145°
Subtract the smaller bearing from the larger: 215°?145°=70°. That gives the acute angle between the two lines of sight. Bearings difference is always clockwise subtraction. More on angle between bearings at Online Math Learning.
Points Q and R are located from P on bearings of 045° and 135°, at distances of 10 km and 20 km respectively. What is the distance between Q and R (to the nearest tenth of a km)?
22.4 km
10.0 km
29.1 km
25.0 km
The angle at P between Q and R is 135°?45°=90°. By the Pythagorean theorem, QR=?(10²+20²)=?500?22.3607, rounding to 22.4 km. This uses right-angle triangle trigonometry. See proof at Maths Is Fun: Pythagoras.
A ship sails 15 km on bearing 120° from port P, then 10 km due west. What is the bearing of its final position from P (to the nearest degree)?
202°
160°
210°
190°
First move gives ?E=15 sin120?12.99, ?N=15 cos120??7.5. Then west shift gives ?E?=10. So total ?E?2.99, ?N??7.5. Bearing=180+arctan(2.99/7.5)?201.8°, rounding to 202°. Calculation details at Khan Academy.
At A, the bearing to B is 150° (AB=8 km). At B, the bearing to C is 350° (BC=10 km). What is the bearing of C from A (to the nearest degree)?
38°
48°
58°
68°
Compute A?B: (8 sin150,8 cos150)?(4,?6.93). Then B?C:add (10 sin350,10 cos350)?(?1.74,9.85). Total A?C?(2.26,2.92). Bearing=arctan(2.26/2.92)?37.9°, rounding to 38°. See vector bearings at Varsity Tutors.
A triangle has vertices A(0,0), B(5,0), C(3,4). What is the bearing of C from A (to the nearest degree)?
37°
53°
127°
323°
From A, ?E=3, ?N=4. Bearing=arctan(3/4)?36.87°, rounding to 37°. Bearings are arctan(East/North). For coordinate bearings see MathCentre PDF.
A plane flies from X to Y on bearing 250° for 100 km, then to Z on bearing 340° for 80 km. What is its straight-line distance from X (to the nearest km)?
128 km
100 km
180 km
64 km
Compute displacements and sum: ?E=100 sin250+80 sin340??121.3, ?N=100 cos250+80 cos340?41.0; distance=?(121.3²+41.0²)?128 km. This uses vector addition. Details at Education.com: Vector Addition.
What is the back bearing of 237°?
57°
417°
237°
60°
The back bearing is 180° different: 237°?180°=57°. If the result is negative add 360°, but here it remains positive. See back bearing rules at BBC Bitesize.
A hiker walks 5 km on bearing 080°, then 3 km on bearing 190°, then 4 km on bearing 300°. What is his bearing back to the start (to the nearest degree)?
265°
85°
174°
264°
Sum the vectors: ?E?0.94, ?N??0.086. Since N is slightly negative and E positive, the bearing is 180+arctan(0.94/0.086)?264.8°, rounding to 265°. Vector bearing methods at Khan Academy.
An observer at (0,0,10) spots a tower at (100,200,50). Ignoring elevation, what bearing should they head for directly (to the nearest degree)?
27°
63°
153°
333°
Ignoring vertical difference, ?E=100 and ?N=200 so bearing=arctan(100/200)?26.6°, rounding to 27°. Elevation doesn’t affect compass direction. See 3D bearing intro at Wikipedia: Azimuth.
What is the initial great-circle bearing from London (51.5074 N, 0.0000 W) to New York (40.7128 N, 74.0060 W)?
288°
270°
295°
310°
Great-circle navigation uses a spherical Earth model. Applying the haversine and bearing formulas gives an initial bearing of approximately 288° from London to New York. See the full derivation at Movable Type Scripts: Great-circle.
What is the initial great-circle bearing from Cape Town (33.9249 S, 18.4241 E) to Port Louis (20.1609 S, 57.5012 E)?
78°
163°
258°
341°
Using spherical trigonometry on lat/long coordinates yields an initial bearing of about 78° from Cape Town to Port Louis. This calculation relies on the great-circle bearing formula. Details are available at Movable Type Scripts.
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Study Outcomes
Calculate precise bearings -
Apply sine, cosine, and tangent ratios to compute unknown bearings and distances in trigonometry problems.
Interpret compass directions -
Convert compass-based directions into angular bearings relative to north or south to understand orientation.
Apply trigonometric ratios -
Use trigonometric functions to solve bearing problems and strengthen your understanding of bearings in trig.
Solve navigation scenarios -
Determine practical routes and distances by modeling real-world navigation problems with trigonometric bearings.
Analyze problem-solving strategies -
Compare different methods for tackling bearing questions and choose the most efficient approach.
Validate calculations -
Cross-verify your answers through alternative trigonometric approaches or graphical checks to ensure accuracy.
Cheat Sheet
Compass Bearings Fundamentals -
Understanding that bearings in trig are measured clockwise from north (e.g., a bearing of 045° points northeast) is essential for navigation tasks. University geospatial resources like those from the UK Hydrographic Office emphasize drawing north - south reference lines and marking angles accurately.
Converting Bearings to Trig Angles -
To apply sine and cosine functions, convert bearings into standard position angles: θ = 90° - bearing for angles east of north or θ = bearing - 90° for angles south of east. MIT's OpenCourseWare recommends sketching both compass and Cartesian axes to avoid sign errors.
Resolving Components with SOH-CAH-TOA -
Break a bearing into north - south and east - west components using sin θ for opposite and cos θ for adjacent parts of a right triangle. This method, highlighted by Khan Academy, simplifies distance and displacement calculations in navigation problems.
Applying the Law of Sines and Cosines -
For non-right-angled bearing problems, use the Law of Sines (a/sin A = b/sin B) or the Law of Cosines (c² = a² + b² - 2ab cos C) to find unknown sides and angles. Royal Institute of Navigation materials show how this handles complex bearing paths between multiple waypoints.
Triangulation via Cross-Bearings -
Determine an unknown position by plotting two bearings from known stations and finding their intersection point. The US National Geospatial-Intelligence Agency demonstrates this cross-bearing technique in surveying to pinpoint locations with high precision.
