31. In a triangle whose sides are a, b
    and c and 8 , where R
    is the radius of its circumscribed circle.
    Which one of the following is correct?
    (a) the triangle is isosceles (b) the
    triangle is right angled (c) the triangle
    is equilateral (d) the triangle is oblique


32. In a triangle ABC, b sin B= c sin C,
    then which one of the following is
    correct?
    (a) the triangle is right angled (b) the
    triangle is isosceles (c) the triangle is
    equilateral (d) the triangle is scalene


33. In a triangle a= √ +1, B= 30, C=
    45 . What is the value of side c?

(a) (√ ) (b) 1 (c) √ (d) 2

34. In the triangle ABC, if b+c= 3a, what

is the value of cot^ cot^?

(a) 1 (b) 2 (c) 3 (d) - 2

35. In a triangle ABC, a= 2b, and
    A=3B. Which one of the following is
    correct?
    (a) the triangle is isosceles (b) the
    triangle is equilateral (c) the triangle is
    right angled (d) Such triangle does not
    exist


36. In a triangle ABC, if A:B:C=
    1:2:3, then what is BC:CA:AB?

(a) 1:2:3 (b) 1: (^) √ :2 (c) 2: (^) √ (d)
√^

37. If the perimeter of the triangle ABC
    is 30cm, then what is the value of a
    (C/2)+c (A/2)?
    (a) 15cm (b) 10cm (c) 15/2 cm (d)
    13cm

HEIGHT AND DISTANCE

1. A vertical tower stands on a
   horizontal plane and is surmounted by
   a vertical flag-staff of height h. At a
   point P on the plane, the angle of
   elevation of the bottom of the flag-staff
   is β and that of the top α. What is the
   height of the tower?

(a) (b) (c)

(d)
( )^

2. An aeroplane flying at a height of
   300m above the ground passes
   vertically above another plane at an
   instant when the angles of elevation of
   two planes from the same point on the
   ground are 60 and 45, respectively.
   What is the height of the lower plane
   from the ground?
   (a) 50m (b)^ √ m (c) 100√ m (d)
   150(√ )m