# 1.A tree standing on a horizontal plane is leaning towards east. At two points situated 30m and 45 m exactly due west on it, the angles of elevation of top are respectively 45 degrees and 30 degrees. Find the height of the top from the ground? 2.A man standing at a height of 20 m long tree situated on a small Island in the middle of a river, observes two poles directly opposite to each other on the two banks of a river. If the angle of depression of the feet of the poles from a point at which man is sitting on the tree on either side of the river are 60 degrees and 30 degrees respectively, find the width of the river? 3.The angle of elevation of top of a tower as observed from a point in a horizontal plane through the foot of the tower is 32 degrees. When the observer moves towards the tower a distance of 100m, he find the angle of elevation of the top to be 63 degrees. Find the height of the tower and distance of the first position from the tower. 4.The shadow of a 60m tree is 18 m. What will be the height of a tree whose shadow is 24 m long a the same time of the day? 5.A man finds the angle of elevation of a tower to be 60 degree. When he walks away a distance of 50m, he finds the angle to be 30 degrees. Find the height of the tower?

### Asked by naresh sudharshana | 23rd Jul, 2013, 11:23: PM

### Please ask one question/query. Please find answer to your first question below.
Here in this case -- a= 30m, b = 45m, angle A = 45 and angle B = 30

Let PQ be the leaning tree and R and S be the two given points at distances *a* and *b* from P respectively.

Let PT = *x *and QT = *h*.

In ?PQT,

In ?QRT,

Substituting the value of *x* from (1), we get

In ?QST,

Substituting the value of *x* from (1), we get

Subtracting equation (2) from (3), we get

Hence subsituting for a= 30m, b = 45m, angle A = 45 and angle B = 30

h = (45-30) / cot30-cot45

h = 15/(root(3) - 1)

h = 20.49 m

Let PQ be the leaning tree and R and S be the two given points at distances *a* and *b* from P respectively.

Let PT = *x *and QT = *h*.

In ?PQT,

In ?QRT,

Substituting the value of *x* from (1), we get

In ?QST,

Substituting the value of *x* from (1), we get

Subtracting equation (2) from (3), we get

Hence subsituting for a= 30m, b = 45m, angle A = 45 and angle B = 30

h = (45-30) / cot30-cot45

h = 15/(root(3) - 1)

h = 20.49 m

### Answered by | 26th Jul, 2013, 05:12: AM

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