Home
Class 12
MATHS
Let a vertical tower AB have its end A o...

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If `∠BPC = beta`, then tan `beta` is equal to

A

`(6)/(7)`

B

`(1)/(4)`

C

`(2)/(9)`

D

`(4)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let AB = h, then AP = 2h
and AC = B C = `(h)/(2)`
Again, let `angleCPA = alpha`

Now, in `angleABP, tan (alpha+beta)=(AB)/(AP) = (h)/(2h)=(1)/(2)`
Also, in `DeltaACP, tan alpha = (AC)/(AP) = (2)/(2h) = (1)/(4)`
Now, `tanbeta = tan[(alpha+beta)-alpha]`
`=(tan(alpha+beta)-tanalpha)/(1+tan(alpha+beta)tanalpha)=((1)/(2)-(1)/(4))/(1+(1)/(2)xx(1)/(4))=((1)/(4))/((9)/(8))=(2)/(9)`
Promotional Banner

Similar Questions

Explore conceptually related problems

AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP = 3AB and C Is the midpoint of AB. If AC and CB subtend angles alpha and beta , respectively, at P, then the value of tan beta is

PQ is a vertical tower having P as the foot. A,B,C are three points in the horizontal plane through P. The angles of elevation of Q from A,B,C are equal and each is equal to theta . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is del . Then prove that the height of the tower is (abc) tantheta/(4)dot

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot

Let alpha" and "beta be the roots of the equation px^(2)+qx+r=0 . If p,q, r in A.P. and alpha+beta=4 , then alpha beta is equal to

Two parallel towers A and B of different heights are at some distance on same level ground. If angle of elevation of a point P at 20 m height on tower B from a point Q at 10 m height on tower A is theta and is equal to half the-angle of elevation of point R at 50 m height on A from point P on B , then sine of theta is

A vertical tower PQ subtends the same anlgle of 30^@ at each of two points A and B ,60 m apart on the ground .If AB subtends an angle of 120^@ at p the foot of the tower ,then find the height of the tower .

AB is a vertical pole with B at the ground level and A at the top . A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^@ . He moves away from the pole along the line BC to a point D such that CD = 7 m . from D the angle of elevation of the point A is 45 then the height of the pole is

The straight line cuts the coordinate axes at A and B. if the mid point of AB is (3,2) the find the equation of AB.

In a triangle OAB ,E is the mid point of OB and D is the point on AB such that AD:DB=2:1 If OD and AE intersect at P then determine the ratio of OP: PD using vector methods

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.