MCQ in Spherical Trigonometry Part 1 | ECE Board Exam Practice

Multiple Choice Questions in Spherical Trigonometry – Part 1 | ECE Board Exam Practice

Spherical trigonometry is one of those topics that catches a lot of ECE reviewees off guard. Unlike plane trigonometry, it deals with triangles drawn on the surface of a sphere, and the rules are different enough to trip you up if you haven’t spent enough time with it before exam day.

This is Part 1 of the Spherical Trigonometry MCQ Series on Pinoybix, put together to help electronics engineering students build familiarity with one of the more challenging areas in the Engineering Mathematics section of the ECE Board Exam. Every question here was compiled from past ECE Board Exam problems, engineering mathematics textbooks, academic journals, and other references that have proven reliable over the years.

Work through each item seriously. This is not the kind of topic you can wing on exam day based on instinct alone. The concepts need to be practiced repeatedly until the approach feels natural and the formulas come to you without hesitation.

If this is your first time encountering spherical trigonometry in your review, take it slow. Read each question carefully, attempt a solution before checking the answer, and make a note of every item that gives you trouble. Those are the ones that deserve the most attention.

Start here and build from the ground up. The goal is understanding, not just finishing the set.

Multiple Choice Questions Topic Outline

MCQ in Solution to Right Triangles | MCQ in Napier’s Rules | MCQ in Solution to Oblique Triangles | MCQ in Area of Spherical Triangles | MCQ in Terrestrial Sphere

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each question.

Problem 1:

If Greenwich Mean Time (GMT) is 6 A.M., what is the time at a place located 30° East longitude?

A. 7 A.M.

B. 8 A.M.

C. 9 A.M.

D. 4 A.M.

Problem 2:

If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?

A. 1 hour and 12 minutes

B. 1 hour and 5 minutes

C. 1 hour and 8 minutes

D. 1 hour and 10 minutes

Problem 3:

One degree on the equator of the earth is equivalent to?

A. 1 minute

B. 4 minutes

C. 30 minutes

D. 1 hour

Problem 4: CE Board April 1997

A spherical triangle ABC as an angle C = 90° and sides a = 50º and c = 80°. Find the value of “b” in degrees.

A. 73.22°

B. 74.33°

C. 75.44°

D. 76.55°

Problem 5:

Solve the remaining side of the spherical triangle whose given parts are A = B = 80° and a = b = 89°.

A. 158° 12’

B. 162° 21’

C. 168° 31’

D. 172° 12’

Problem 6:

Solve for the side b of a right spherical triangle ABC whose parts are a = 46°, c = 75° and C = 90°.

A. 72°

B. 68°

C. 48°

D. 74°

Problem 7:

Given the right spherical triangle whose given parts are a = 82°, b = 62° and c = 90°. What is the value of the side opposite the right angle?

A. 84° 30’

B. 84° 45’

C. 86° 15’

D. 85° 15’

Problem 8:

Determine the value of the angle B of an isosceles spherical triangle ABC whose given parts are b = c = 54° 28’ and a = 92° 30’.

A. 89° 45’

B. 55° 45’

C. 84° 25’

D. 41° 45’

Problem 9:

Solve for angle A in the spherical triangle ABC, given a = 106º 25’, c = 42° 16’ and B = 114° 53’.

A. 45° 54’

B. 80° 42’

C. 97° 09’

D. 72° 43’

Problem 10:

Solve for angle C of the oblique triangle ABC given, a = 80°, c = 115° and A = 72º.

A. 61°

B. 85°

C. 95°

D. 119°

Problem 11:

Determine the spherical excess of the spherical triangle ABC given a = 56°, b = 65º and c = 78°.

A. 33° 33’

B. 68° 37’

C. 91° 57’

D. 98° 45’

Problem 12:

What is the spherical excess of a spherical triangle whose angles are all right angles?

A. 45°

B. 90°

C. 60°

D. 30°

Problem 13: ECE Board April 1997

The area of a spherical triangle ABC whose parts are A = 93º 40’, B = 64° 12’, C = 116º 51’ and the radius of the sphere is 100 m is?

A. 15613 sq. m.

B. 16531 sq. m.

C. 18645 sq. m.

D. 25612 sq. m.

Problem 14:

A spherical triangle has an area of 327.25 sq. km. What is the radius of the sphere if its spherical excess is 30º?

A. 20 km

B. 22 km

C. 25 km

D. 28 km

Problem 15: EE Board April 1997

A ship on a certain day is at latitude 20º N and longitude 140º E. After sailing for 150 hours at a uniform speed along a great circle route, it reaches a point at latitude 10º S and longitude 170º W. If the radius of the earth is 3959 miles, find the speed in miles per hour.

A. 17.4

B. 15.4

C. 16.4

D. 19.4

16. Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40°, 65°, and 110°.

A. 12.34 sq. m.

B. 14.89 sq. m.

C. 16.45 sq. m.

D. 15.27 sq. m.

17. A right spherical triangle has an angle C = 90°, a = 50°, and c = 80°. Find the side b.

A. 45.33°

B. 78.66°

C. 74.33°

D. 75.89°

18. If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at 120° East longitude?

A. 6 p.m.

B. 4 am

C. 4 p.m.

D. 6 am

19. An airplane flew from Manila (14° 36’N, 121° 05’E) at a course of S 30° E maintaining a certain altitude and following a great circle path. If its groundspeed is 350 knots, after how many hours will it cross the equator?

A. 2.87 hours

B. 2.27 hours

C. 3.17 hours

D. 3.97 hours

20. Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14° 36’N latitude and 121° 05’ E longitude. San Francisco is situated at 37° 48’ N latitude and 122° 24’ W longitude.

A. 7856.2 nautical miles

B. 5896.2 nautical miles

C. 6326.2 nautical miles

D. 6046.2 nautical miles

21. An isosceles spherical triangle has angle A=B=54° and side b=82°. Find the measure of the third angle.

A. 157°52’12”

B. 160°05’20”

C. 158°18’43”

D. 155°42’50”

22. Find the distance in nautical miles and the time difference between Tokyo and Manila if the geographical coordinates of Tokyo and Manila are (35.65° N lat. ; 139.75°E long.) and (14.58°N lat. ; 120.98°E long.) respectively.

A. 1.25 hours

B. 1.35 hours

C. 1.15 hours

D. 1.05 hours

23. If Greenwich Mean Time (GMT) is 9 AM, What is the time in a place 45° W of longitude?

A. 5:30 AM

B. 6:15 AM

C. 5:45 AM

D. 6:00 AM

24. If Greenwich Mean Time (GMT) is 7 A.M. What is the time in a place located at 135°E longitude?

A. 3:45 PM

B. 4:15 PM

C. 3:30 PM

D. 4:00 PM

25. Considering the earth as a sphere of radius 6400 km. Find the area of a spherical triangle on the surface of the earth whose angles are 50°, 89° and 120°.

A. 55,321,098.12 km²

B. 56,476,062.07 km²

C. 57,812,345.19 km²

D. 54,987,654.23 km²

26. In a spherical triangle ABC, A = 116°19’, B = 55°30’, and C = 80°37’. Find the value of side a.

A. 112°42′

B. 118°23′

C. 115°57’

D. 110°15′

Online Questions and Answers in Spherical Trigonometry Series

Following is the list of multiple choice questions in this brand new series:

Online Questions and Answers in Plane Trigonometry

Mathematics Board Examination Mastery | Math Engineering Pre-Board