MCQ in Spherical Trigonometry Part 1 – Answer Key | ECE Board Exam

You’ve worked through Part 1 of the Spherical Trigonometry MCQ Series. Now comes the part that actually makes your review count.

This answer key covers every item in Part 1, compiled from past ECE Board Exam problems, engineering mathematics textbooks, academic journals, and other references that serious reviewees have relied on for years. The answers are here to help you do more than just check if you got it right. They are here to help you understand exactly where your thinking was solid and where it needs more work.

Spherical trigonometry is not a topic that rewards guessing. The formulas are specific, the applications are precise, and the margin for error on the actual board exam is thin. If you got an item wrong, don’t just note it and move on. Go back to the question, trace your solution step by step, and figure out where the reasoning broke down. That kind of honest review is what separates people who pass from people who have to come back and try again.

If you jumped straight to this answer key without going through the questions first, close this page and do the work. Come back here after. The answers mean nothing if you haven’t wrestled with the problems on your own first.

1. B. 8 A.M.

Solution: What is the time at a place located 30° East longitude?

2. A. 1 hour and 12 minutes

Solution: What is the time difference between Tokyo and Manila?

3. B. 4 minutes

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

4. B. 74.33°

Solution: Find the value of “b” in degrees of a spherical triangle ABC

5. C. 168º 31’

Solution: Solve the remaining side of the spherical triangle

6. B. 68°

Solution: Solve for the side b of a right spherical triangle ABC

7. C. 86° 15’

Solution: What is the value of the side opposite the right angle?

8. D. 41° 45’

Solution: Determine the value of the angle B of an isosceles spherical triangle ABC

9. C. 97° 09’

Solution: Solve for angle A in the spherical triangle ABC

10. D. 119°

Solution: Solve for angle C of the oblique triangle ABC

11. A. 33° 33’

Solution: Determine the spherical excess of the spherical triangle ABC

12. B. 90°

Solution: What is the spherical excess of a spherical triangle?

13. B. 16531 sq. m.

Solution: What is the area of a spherical triangle ABC?

14. C. 25 km

Solution: What is the radius of the sphere if its spherical excess is 30°?

15. C. 16.4

Solution: If the radius of the earth is 3959 miles, find the speed in miles per hour

16. D. 15.27 sq. m.

Solution: Calculate the area of a spherical triangle whose radius is 5 m

17. C. 74.33°

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

18. C. 4 p.m.

Solution: What is the time in the Philippines, which is located at 120° East longitude?

19. A. 2.87 hours

Solution: If its groundspeed is 350 knots, after how many hours will it cross the equator?

20. D. 6046.2 nautical miles

Solution: Find the distance in nautical miles between Manila and San Francisco

21. C. 158°18’43”

Solution: An isosceles spherical triangle has angle A=B=54° and side b=82°

22. A. 1.25 hours

Solution: Find the distance in nautical miles and the time difference

23. D. 6:00 AM

Solution: What is the time in a place 45° W of longitude?

24. D. 4:00 PM

Solution: What is the time in a place located at 135°E longitude?

25. 56,476,062.07 km²

Solution: Find the area of a spherical triangle on the surface of the earth

26. C. 115°57’

Solution: In a spherical triangle ABC, A=116°19’, B=55°30’, and C=80°37’

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

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