If the
angles of elevation of the top of a tower from three collinear points A, B
and C, on a line leading to the foot of the tower, are `30^0`
, `45^0`
and `60^0`
respectively, then the ratio, AB : BC, is :
(1) `sqrt(3):1`
(2)
`sqrt(3):sqrt(2)`
(3)
`1:sqrt(3)`
(4)
`2"":""3`
A
`sqrt(3):1`
B
`sqrt(3):sqrt(2)`
C
`1:sqrt(3)`
D
`2:3`
Text Solution
AI Generated Solution
To solve the problem, we need to find the ratio \( AB : BC \) given the angles of elevation of the top of a tower from three collinear points A, B, and C.
### Step-by-step Solution:
1. **Define the Variables**:
- Let the height of the tower be \( h \).
- Let \( D \) be the foot of the tower.
- Let \( A \), \( B \), and \( C \) be the points from which the angles of elevation are measured, with \( A \) being the farthest point from the tower and \( C \) being the closest.
...
The angle of elevation of the top of a tower from two distinct points s and t from foot are complementary. Prove that the height of the tower is sqrt[st] .
The angle of elevation of the top of a T.V. tower from three points A,B,C in a straight line in the horizontal plane through the foot of the tower are alpha, 2alpha, 3alpha respectively. If AB=a, the height of the tower is
The angle of elevation of the top of a tower from a point on the ground is 30^(@) . After walking 40sqrt3 m towards the tower, the angle of elevation becomes 60^(@) . Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground 50m away from the foot of the tower is 45^0dot Then the height of the tower (in metres) is 50sqrt(3) (b) 50 (c) (50)/(sqrt(2)) (d) (50)/(sqrt(3))
If the angles of elevation of a tower from two points distant a and b (a > b) from its foot and in the same straight line with it are 30^@ and 60^@ , then the height of the tower is (a) sqrt(a+b) (b) sqrt(a b) (c) sqrt(a-b) (d) sqrt(a/b)
A tower subtends angle theta, 2theta, 3theta at the three points A,B and C respectively lying on a horizontal line through the foot of the tower. Then AB/BC is equal to
The value of sqrt(3-2\ sqrt(2)) is (a) sqrt(2)-1 (b) sqrt(2)+1 (c) sqrt(3)-sqrt(2) (d) sqrt(3)+\ sqrt(2)
The angles of the depression of the top and bottom of the tower is seen from the top of a 60sqrt(3) cliff are 45^alpha and 60^alpha respectively. Find the height of the tower.
The angles of the depression of the top and bottom of the tower is seen from the top of a 60sqrt(3) cliff are 45^alpha and 60^alpha respectively. Find the height of the tower.
The angles of the depression of the top and bottom of the tower is seen from the top of a 60sqrt(3) cliff are 45^alpha and 60^alpha respectively. Find the height of the tower.
