In the given diagram,AB represents a vertical pole and CD represents a 40 m high tower both of which are standing on the same horizontal plane.From the top of the tower,the angles of depression of the top and the foot of the pole are 24 degrees,30 inches and 48 degrees,30 inches respectively.calculate
(i) the horizontal distance between the pole and the tower
(ii) the height of the pole
Tough to figure out from the "non-given" diagram.
let DB, the horizontal distance be x.
angle ADB = 48 degrees, 30 minutes (not inches!)
= 48.5°
so tan 48.5 = 40/x
x = 40/tan48.5 = 35.39 m
from C, draw a horizontal to meet AB at E
tan 24.5 = AE/x
AE = xtan24.5 = 16.13 m
so height of pole = BE = 40-16.128 = 23.87 m
To solve this problem, we can use trigonometry and the given angles of depression. Here's how we can calculate the answers:
(i) To find the horizontal distance between the pole and the tower, we can use the tangent function.
Let x be the horizontal distance between the pole and the tower.
Using the angle of depression of 24 degrees, we have:
tan(24) = (CD - AB) / x
Since AB is the height of the pole and CD is the height of the tower, we can rewrite the equation as:
tan(24) = (40 - AB) / x
Similarly, using the angle of depression of 48 degrees and 30 inches, we have:
tan(48) = (CD + AB) / x
Rewriting the equation with the given values, we have:
tan(48) = (40 + AB) / x
Now we have two equations with two unknowns (AB and x). We can solve this system of equations to find the values of AB and x.
(ii) To find the height of the pole (AB), we can use the angle of depression of 30 degrees and 30 inches.
Using the angle of depression of 30 degrees, we have:
tan(30) = AB / x
We can use the value of x obtained from part (i) and solve for AB.
By solving these equations simultaneously, we can find the horizontal distance between the pole and the tower (x) and the height of the pole (AB).