`angle ABD = 54^@ and angleBCD = 43^@`, calculate the `angleACD`

angle ABD = 54^@ and angleBCD = 43^@ , calculate the angleBAD

angle ABD = 54^@ and angleBCD = 43^@ , calculate the angleBDA

In the fig side BC of triangleABC is produced to angleACD=128^@ and angleABC=43^@ find angleBAC and angleACB .

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.If angleDBC = 70^@ and angle BAC = 30^@ find angleBCD

In Fig. 6.43, if PQ bot PS , PQ || SR, angle SQR = 28^@ and angle QRT = 65^@ , then find the values of x and y.

A ray of light passes from air to glass (mu = 1.5) at an angle of 30^@ .Calculate angle of refraction.

A ray of light suffers minimum deviation,while passing through a prism of refractive index 1.5 and refracting angle 60^@ ,calculate the angle of deviation and angle fo incidence.

In any DeltaABC, if D be any points of the base BC such that (BD)/(DC)=m/n and angle ABD =alpha, angle DAC =beta,angle CDA=thetaand AD=x then prove that (m+n) ^(2). x =(m+n) (mb^(2) +nc^(2))-mna^(2)

A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45^@ and the angle of depression of the base is 30^@ . Calculate the distance of the cliff from the ship and the height of the cliff.

A man on the deck of a ship is 12 m above water level. He observes that the angle of elevation of the top of a cliff is 45^@ , and the angle of depression of the base is 30^@ . Calculate the distance of the cliff from the ship and the height of the cliff.