This is the Multiple Choice Questions Part 1 of the Series in Spherical Trigonometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

### 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 I of the Series

**Choose the letter of the best answer in each questions.**

**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

18. 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

### Online Questions and Answers in Spherical Trigonometry Series

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

**Spherical Trigonometry MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

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I badly need the solution of number 20. Where can I see it?

I also seek a solution for number 20