P and Q are two places on the equator.
The shortest distance between them along the equator is 8500 km.
Find the angle between P and Q.
(Take R =6,370 km, π= 3.142)

Three cities London, Seoul and Harare are such that Seoul is located 50 km away from London on a bearing of 065°.
Harare is 100 km away from London on a bearing of 305°.
The distance between Seoul and Harare is

Three locations on the surface of the earth are Mumbai(45°N, 20ºE), Guanzhou(45°N, 40°E) and Ibadan(45°S, 40°E). Which of the following statements are correct?
I. Guanzhou and Ibadan are on the same longitude.
II. Guanzhou and Ibadan are on the same latitude.
III. The difference between the longitudes of Mumbai and Guanzhou  is 60°.
IV. The difference between the latitudes of Mumbai and Ibadan is 90°.

A bearing of 310°, expressed as a compass bearing is

The value of
is

A right-angled triangle has sides of lengths (3m-1) cm, (m) cm and (3m+1) cm.
The value of m is

The value of
1 + sec²60° is

Starting from town X(45°N, 17°E), an airplane flies to town Y(45°N, 47°E) along the parallel of latitude and later to a third town Z(60°N, 47°E) along the meridian.
(R = 6,370 km, π= 22/7).
The distance between Y and Z along the meridian is

Point P(60°S,22°E) lies on the same latitude as point Q.
If the distance PQ measured along the parallel of latitude is 5,oo5 km,
the radius of the earth is 6.370 km and π = 22/7,
the longitude of point Q is

If sin θ = a/b, where θ is an acute angle,
then cot θ equals

From the top of a 100m high building, a man observes the top of a tree at an angle of depression of 30°.
If the tree is 50 m tall, the angle of depression of the foot of the tree as viewed by the man is

If cos θ = 4/5,
then for 0° < θ < 90°,
tanθ is equal to

If there is no stop-over at Dubai, and the average speed of the airplane is 500km/hr, the total time taken for the plane to fly from Lagos to Kuala Lumpur via Dubai is approximately

If cos θ = -½,
the values of θ could be

A woman 1.65 m tall stood 50 m away from the foot of a tower and observed that the angle of elevation pf the top of the tower to be 50°. What is the height of the tower?

Given that tan²θ + sec²θ = 3,
the value of θ
(for 0°<θ<90°) is

If cos θ = √3/2, evaluate 

If cos θ = sin 50°,
then θ is

The angle between latitudes 20°N and 74°N is

The values of θ for which
sin θ = cos θ are within the range 0° < θ < 360°

The bearing of a point P from an observer Q is S37°W.
The bearing of Q from P is

The values of tan 225° and tan 315° are respectively

X and Y are two lakes on the earth's surface.
X has a latitude 34°N and Y has latitude 15°S.
If the lakes are on the same meridian ,
calculate the distance between them along the meridian
(Take 2πR = 40,000 km)

In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm.
Find |PR|

The two perpendicular sides of a right-angled triangle are 9 cm and 12 cm in length.

The smallest angle of the triangle is