From the top of a tower the angle of depression of an object on the horizontal ground is found to be 60degree. On descending 20 m vertically downwards from the top of the tower, the angle of depression of the object is found to be 30degree Find the height of the tower.
To find the height of the tower, we can use trigonometry.
Let's denote the height of the tower as 'h' and the horizontal distance between the object and the base of the tower as 'x'.
From the given information, we have two right-angled triangles: one formed by the tower, the object, and the horizontal ground, and another formed by the tower, the object, and the point 20 meters below the top of the tower.
In the first triangle, the angle of depression is 60 degrees, and in the second triangle, the angle of depression is 30 degrees.
Using the tangent function, we can relate the tangent of an angle to the opposite and adjacent sides of a right-angled triangle.
In the first triangle:
tan(60) = h/x
In the second triangle:
tan(30) = (h - 20)/x
Now we can solve these two equations simultaneously to find the value of 'h'.
First, let's find the value of 'x' by equating the right-hand sides of the two equations:
h/x = (h - 20)/x
By canceling 'x' from both sides of the equation, we get:
h = h - 20
This equation implies that 'h' is equal to its own value decreased by 20, which is not possible.
Hence, there is no solution for this problem. It seems there is a contradiction in the given information or a mistake in the problem statement.
Rats!!
Just have to get better glasses, I read the 30° as 35°
Just how do you spot those little typos? Amazing.
good work, but - where did the 35° come from?
make your sketch
label the top of the tower A, bottom of tower B,
object on ground C and the point 20 m from the top as D
in triangle ACD
angle ACD = 60° - 35° = 25°
angle A = 180° - 90° - 60° = 30°
and AD = 20
by the sine law
CD/sin30 = 20/sin25
CD = 20sin30/sin25
in the right-angled triangle DCB
sin35 = DB/CD
DB = CDsin35
= 20sin30 sin35/sin25 , notice I have not yet touched my calculator , now I will
= 13.57
so the height of the tower is 20+13.57 = 33.57 m