
The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be . After moving a distance of 2 meters from P towards the foot of the tower, the angle of elevation changes to . Then the height (in meters) of the tower is:
(A) (B) (C) (D)
Answer
518.1k+ views
Hint: Analyze the situation with a diagram. Use trigonometric ratios to find the distance of point P from the foot of the tower in both cases. And then compare both values to get the desired result.
Complete step-by-step answer:
Consider the above figure, let L be the initial distance of the foot of the tower from point P and h be the height of the tower.
As per the information given in the question, is the angle of elevation of the top of the tower from point P.
From shown above:
Now, after moving 2 meters towards the tower we reach another point Q. Then the distance between the foot of the tower and point Q is . And the angle of elevation of the top of the tower from point Q is given in the question as . So in in the above figure:
Now, comparing equation and , we have:
Taking as LCM, we’ll get:
Now we know that, , applying this we’ll get:
We know that, , applying this formula, we’ll get:
Therefore, the height of the tower is . Option (C) is correct.
Note: We can use any of the trigonometric ratios to get the end results. But in this case, perpendicular and base are known for the given angles so it is convenient to use either . If we want to use any other trigonometric ratios, then we have to determine hypotenuse first by using Pythagoras theorem.
Complete step-by-step answer:

Consider the above figure, let L be the initial distance of the foot of the tower from point P and h be the height of the tower.
As per the information given in the question,
From
Now, after moving 2 meters towards the tower we reach another point Q. Then the distance between the foot of the tower and point Q is
Now, comparing equation
Taking
Now we know that,
We know that,
Therefore, the height of the tower is
Note: We can use any of the trigonometric ratios to get the end results. But in this case, perpendicular and base are known for the given angles so it is convenient to use either
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
State and prove Bernoullis theorem class 11 physics CBSE

What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

State the laws of reflection of light

In northern hemisphere 21st March is called as A Vernal class 11 social science CBSE
