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

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 X and Y along the parallel of latitude in km, is

An observer on the ground views an airplane of altitude 1,000 m at an angle of elevation of 30°.
How far is the plane from the observer?

An airplane flies 100 km on a bearing of 330° and then flies 300 km due West. How far West of the starting point is the plane?

The value of
is

The angle of elevation of the top of a tree from a point P and the ground is 30°. From a point Q, 10 m closer to the foot of the tree, the angle of elevation is 45°.
How tall is the tree?

The value of
sin(870°) is

Three cities Cape Town, Prague and Tbilisi are such that Prague is located 50 km away from Cape Town on a bearing of 065°.
Tbilisi is 100 km away from Cape Town on a bearing of 305°.
The bearing of Tbilisi from Prague is approximately

The latitudes on which the radius of the parallel of latitude is one-half of the earth's radius are

sin 38° has the same value as

Sin 38° has the same value as

If the radius of the earh is 6,370 km, the distance between two towns on latitudes 25°N and 20°S on the same meridian is (π = 22/7)

Given that
cos²θ - sin²θ = 1/8,
find the value of tan θ

The hypotenuse of a right-angled isosceles triangle is 8 units.
The length of each of the other sides are

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

The bearing of a point P from a point Q is 065°.
What is the bearing of Q from P?

Which of the following have the same value as sin 15°?
I. sin 165°
II. sin 285°
III. sin (-15°)
IV. sin (-195°)

An observer standing on the top of a building 40 m high views a stone on the ground level at an angle of depression of 38°.
The distance of the stone from the foot of the building in metres, is equal to

Points X and Y are respectively 48m North and 20m East of point Z, The bearing of X and Y is approximately

If sinθ = 1/2 and 0° < θ < π/2, evaluate

Without using tables,
evaluate sin(- 1320°)

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°.

Two towns P(θ°N, 7°E) and Q(θ°N, 29°W) are separated by a distance of 2,002 km, measured along the parallel of latitude.
If R = 6,370 km and π = 22/7,
the value of θ is

The value of
sin (870°) is

An inelastic string of length 1.0 m anchored to a point X has a stone tied to the end Y.
How high does the stone rise when the string XY is inclined at 30° to the original vertical position?