Question 1: Find the degree corresponding to the following radian measures

Answer:

Question 2: Find the radian measure corresponding to the following degree measures:

Answer:

Question 3: The difference between the two acute angles of a right-angled triangle is radians. Express the angles in degrees.

Answer:

be two acute angles of a right angles triangle.

… … … … … i)

Also in a right angled triangle

… … … … … ii)

Adding i) and ii) we get

Question 4: One angle of a triangle is grades and another is degrees while the third angle is radians. Express all the angles in degrees.

Answer:

Let the three angles be

In the triangle

Question 5: Find the magnitude, in radians and degrees, of interior angle of: i) pentagon ii) octagon (iii) heptagon iv) duodecagon

Answer:

Interior angles of a polygon with sides

i) Pentagon

ii) Octagon

(iii) Heptagon

iv) Duodecagon

Question 6: The angles of a quadrilateral are in A.P. and the greatest angles is . Express the angles in radians.

Answer:

Let the angles of quadrilateral in degrees be

We know, sum of angles in quadrilateral

Largest angle

angles are

,

,

Question 7: The angles of a quadrilateral are in A.P. and the number of degrees in the least angles is to the number of degrees in the mean angle as . Find the angles in radians.

Answer:

be the three angles

It is given that are in an AP

,

Question 8: The angle in a regular polygon is to that in another is and the number of sides in first is twice that in second. Determine the number of sides of two polygons.

Answer:

be the number of sides of two regular polygons respectively.

… … … … … i)

Also

Substituting in i) we get

Hence

Question 9: The angles of a triangle are in A.P. such that the greatest angle is five times the least. Find the angles in radians.

Answer:

be the three angles

In radians

Question 10: The number of sides of two regular polygons are as and the difference between their angles is 9^{\circ}. Find the number of sides of the polygon.

Answer:

be the number of sides of two regular polygons respectively.

Also given

Hence

Question 11: A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by in a distance of

Answer:

be the rail road

Question 12: Find the length which is at a distance m will subtend an angle of at the eye.

Answer:

Question 13: A wheel makes revolutions in a minute. Through how many radians does it turn in second.

Answer:

revolutions per minute revolution per second

revolution, wheel will cover

In one second the wheel will cover

Question 14: Find the angle in radians through which a pendulum swings if its length is and the tip describes as arc of length

Answer:

length of pendulum m

m

m

m

m

Question 15: The radius of a circle is Find the length of an arc of this circle, if the length of the chord of the arc is

Answer:

radius of circle m

chord m

is equilateral triangle.

m

Question 16: A railway train is travelling on a circular curve of m radius at a rate of km/hr. Through what angle has it turned in seconds?

Answer:

radius m

The train turns seconds

m

Question 17: Find the distance from the eye at which a coin of diameter should be held so as to conceal the full moon whose angular diameter is .

Answer:

be the distance at which coin needs to be placed to completely conceal the full moon.

m

Therefore the coin should be placed m away from the eye.

Question 18: Find the diameter of the sun in km supposing that it subtends an angle of at the eye of an observer. Given that the distance of the sun is km.

Answer:

km

Therefore Distance of sun is km

Question 19: If the arcs of the same length in two circles subtend angles at the center, find the ratio of their radii.

Answer:

be two circles with same arc length

are two angles subtended by the arcs on respective circles

Question 20: Find the degree measure of the angle subtended at the center of the circle of radius by an arc of length (Use ):

Answer:

be the angle subtended by the at center