Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan$$\angle$$ACB = $${1 \over 2}$$, then :
Let $${{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}$$, where A, B, C are angles of triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :
A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = $$\sqrt 5 $$ inches and $$\angle$$PCB = tan-1(2). The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is :
A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$ at the eye of the observer A while the angle of elevation of its center from the eye of A is 75$$^\circ$$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :
A
$$8(2 + 2\sqrt 3 + \sqrt 2 )$$
B
$$8(\sqrt 6 + \sqrt 2 + 2)$$
C
$$8(\sqrt 2 + 2 + \sqrt 3 )$$
D
$$8(\sqrt 6 - \sqrt 2 + 2)$$
Explanation
O $$\to$$ centre of sphere
P, Q $$\to$$ point of contact of tangents from A
Let T be top most point of balloon & R be foot of perpendicular from O to ground.
From triangle OAP, OA = 16cosec30$$^\circ$$ = 32
From triangle ABO, OR = OA sin75$$^\circ$$ = $$32{{\left( {\sqrt 3 + 1} \right)} \over {2\sqrt 2 }}$$
So level of top most point = OR + OT
$$ = 8\left( {\sqrt 6 + \sqrt 2 + 2} \right)$$
Questions Asked from Properties of Triangle
On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions