
The angles of depression of top and bottom of a building high as observed from
top of a tower are and , respectively. Find the height of the tower and also
the horizontal distance between the building and the tower.
Answer
527.1k+ views
Hint: The given question is related to heights and distance. Try to recall Try to recall the formulae
related to trigonometric ratios and values of trigonometric functions for standard angles.
The following formulae will be used to solve the given problem:
(a)
(b)
(c)
Complete step by step solution:
Now, considering the information given in the question, we can draw the following figure for better visualization of the problem:
Let be the tower of height meter and be the building of height . Let
meter be the horizontal distance between the building and the tower. We will consider a point
on the tower which is at the same level as the top of the building . So, and
. Also, meter . In the question, it is given that the angle of
depression of top and bottom of the building as seen from the top of the tower are and
respectively. So, , and .
Now, and are horizontal lines. So, they are parallel to each other. So, and are alternate interior angles. So, they will be equal. Also,
and are also alternate interior angles. So, they will
also be equal. So, and .
Now, we will consider .
In ,
Now, we will consider .
In ,
Now, the distance between the tower and the building is the same in both cases. So, .
On cross-multiplying, we get:
Substituting in equation , we get:
Hence, the height of the tower is and the distance between the building and tower is equal
to .
Note: Students are generally confused between the values of and . and . These values should be remembered as they are used in various problems of heights and distances.
related to trigonometric ratios and values of trigonometric functions for standard angles.
The following formulae will be used to solve the given problem:
(a)
(b)
(c)
Complete step by step solution:

Now, considering the information given in the question, we can draw the following figure for better visualization of the problem:
Let
meter be the horizontal distance between the building and the tower. We will consider a point
on the tower
depression of top and bottom of the building as seen from the top of the tower are
Now,
also be equal. So,
Now, we will consider
In
Now, we will consider
In
Now, the distance between the tower and the building is the same in both cases. So,
On cross-multiplying, we get:
Substituting
Hence, the height of the tower is
to
Note: Students are generally confused between the values of
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