A spherical ballon of radius r while floating in the sky, makes an angle `alpha` in the eye of viewer. If the angle of elevation of the centre of the ballon in the eye of the viewer be `beta`, show that the altitude of the centre of the ballon from the ground is `r cosec alpha/2 sin beta`.

A spherical balloon of radius r subtends an angle alpha at the eye of anb observer. If the angle of elevation of the cerntre of the balloon be beta , then prove that the height of the balloon is r cosec (alpha)/(2) sin beta.

A round balloon of radius 10m subtends an angle of 60^@ at the eye of the observer while the angle of elevation of its centre is 30^@ . Which of the following is the height of the centre of the balloon?

From a point a metres above a lake the angle of elevation of a cloud is alpha and the angle of depression of its reflection is beta . Prove tha the height of the cloud is (a sin(alpha + beta))/(sin(beta-alpha)) metres.

A cyclist tilts to make an angle theta with level ground as he takes a circular turn of radius r. If the speed of the cycle is v, show that tan theta = rg/ v^(2)

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

A tower AB leans towards west making an angle alpha with the vertical . The anlgular elevation of B , the topmost point of the tower is beta as obsreved from a point C due east of A at distance d from A.If the angular elevation of B from a pont D at a distance 2d due east of C is gamma , then prove that 2 tan alpha = cot gamma -3cot beta

A disc of mass M and radius R is rolling without slipping down an inclined plane. Show that the acceleration of the centre of mass of the disc is (2)/(3) g sin theta . Given angle of inclination of the plane is theta and moment of inertia of the disc is (MR^(2))/(2) .

A disc of mass M and radius R is rolling without slipping down ay inclined plane. Show that the acceleration of the centre of mass of the disc is 2/3 g sin theta . Given, angle of inclination of the plane is theta and moment of inertia .of the disc is (MR^2)/2

A ladder rest against a wall making an angle alpha with the horizontal. The foot of the ladder is pulled away from the wall through a distance x , so that it slides a distance y down the wall making an angle beta with the horizontal. Prove that x=ytan(alpha+beta)/2dot