Analytic Geometry

Find the angle in mils subtended by a line \(10\) yards long at a distance of \(5000\) yards.

Assuming that the earth is a sphere whose radius is \(6400\) km. Find the distance along a \(3\) degree arc at the equator of the earth's surface.

A rat fell on a bucket of a water wheel with diameter of \(600\) cm which traveled an angle of \(190^\circ\) before it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell.

Given a circle whose diameter AB equals \(2\) m. If two points C and D lie on the circle and angles ABC and BAD are \(18^\circ\) and \(36^\circ\), respectively, find the length of the major arc CD.

A certain angle has a supplement \(5\) times its complement. What is the angle?

Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle.

Given a triangle, \(C = 100^\circ\), \(a = 15\) m, \(b = 20\) m. Find c.

In triangle ABC, angle \(A = 45^\circ\) and \(C = 70^\circ\). The side opposite angle C is \(40\) m long. What is the length of the side opposite angle A?

The sides of a triangle are \(8\) cm, \(10\) cm and \(14\) cm. Determine the radius of the inscribed circle.

What is the radius of the circle circumscribing an isosceles right triangle having an area of \(162\) sq. cm.?

The sides of a triangle are \(8\) cm, \(10\) cm and \(14\) cm. Determine the radius of the circumscribing circle.

Two sides of a triangle are \(50\) m and \(60\) m long. The angle included between these sides is \(30^\circ\). What is the interior angle opposite the longest side?

A circle with radius \(6\) cm has half its area removed by cutting off a border of uniform width. Find the width of the border.

The area of a circle circumscribing about an equilateral triangle is \(254.47\) sq. m. What is the area of the triangle in sq. m?

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side \(10\) cm long?

The area of a triangle inscribed in a circle is \(39.19 \text{ cm}^2\) and the radius of the circumscribed circle is \(7.14\) cm. If the two sides of the inscribed triangle are \(8\) cm and \(10\) cm, respectively, find the third side.

The area of a triangle is \(8346\) sq. m and two of its interior angles are \(37^\circ 25'\) and \(56^\circ 17'\). What is the length of the longest side?

The distance between the centers of the three circles which are mutually tangent to each other externally are \(10\), \(12\) and \(14\) units. The area of the largest circle is

A circle having an area of \(452\) sq. m is cut into two segments by a chord which is \(6\) m from the center of the circle. Compute the area of the bigger segment.

Find the difference of the area of the square inscribed in a semi-circle having a radius of \(15\) m. The base of the square lies on the diameter of the semi-circle.