Spherical Trigonometry

Question 1

A spherical triangle ABC has an angle C = 90°, and sides a = 50° and c = 80°. Find the measure of side b in degrees.

Answer 1

b = 74.33°

Question 2

A spherical triangle ABC has an angle C = 90°, and sides a = 50° and c = 80°. Find the measure of angle A in degrees.

Answer 2

A = 51.07°

Question 3

Given a right spherical triangle ABC with A = 112° and b = 32°. Find side a.

Answer 3

127.32°

Question 4

Given a right spherical triangle ABC with A = 112° and b = 32°. Find side c.

Answer 4

120.94°

Question 5

For a given isosceles spherical triangle A = 75°, B = 75° and b = 84°. Find the value of angle “c”.

Answer 5

135.80°

Question 6

In the spherical triangle ABC, A = 116° 19’, B = 55° 30’ and C = 80° 37’. Find the values of sides a, b and c.

Answer 6

a = 115.57°
b = 56.03°
c = 83.17°

Question 7

A plane flew from Tokyo ( latitude= 14° 30’ N, and longitude = 121° 30’ E ) on a course of S 30° W, and maintains uniform altitude. At what longitude will it cross the equator?

Answer 7

113° 16’ E

Question 8

Compute the distance of Manila ( 14°36’ N, 121°05’ E ) from Hong Kong ( 22°18’ N, 114° 10’ E ). Express your answer in kilometers.

Answer 8

1, 123.61 km

Question 9

The area of the spherical triangle is given by the formula,

Answer 9

A = πr²E/180°

Question 10

Formula of the spherical excess E

Answer 10

E = A + B + C - 180°

Question 11

Convert 1° to NM.

Answer 11

60 NM

Question 12

Convert 1 NM to km.

Answer 12

1.852 km