A boy observes that the angle of elevation of a tower is 32 degree he then walks towards the tower and then discovers that the angle of elevation is 43 degree find the height of the tower
This question is unsolveable without the distance the boy walked towards the tower.
To find the height of the tower, we can use trigonometry. Let's assume the boy's initial distance from the tower is 'x' and the final distance from the tower is 'y'.
From the given information, we have:
Angle of elevation from the initial position = 32 degrees
Angle of elevation from the final position = 43 degrees
Using trigonometry, we can establish the following relationships:
tan(32 degrees) = height of the tower / x
tan(43 degrees) = height of the tower / y
Now, we need to find the value of 'y' with respect to 'x'. To do that, we can equate x/y to the ratio of heights:
(x/y) = (height of the tower / x) / (height of the tower / y)
(x/y) = (tan(32 degrees)) / (tan(43 degrees))
To find the value of 'y', we can rearrange the equation:
y = (x * tan(43 degrees)) / tan(32 degrees)
Now, we have the value of 'y' in terms of 'x'. However, we need to find the height of the tower, not the distance. We can use the right triangle formed by the boy, the tower, and the horizontal ground.
In this triangle, the height of the tower forms the opposite side, and 'y' is the adjacent side. Therefore, the height of the tower can be determined by multiplying the value of 'y' by the height of the boy's eye level (assuming the boy's eye level is at ground level).
Let's say the height of the boy's eye level is 'h'. Then, the height of the tower (H) can be calculated as:
H = y * h
Substituting the value of 'y' from the equation above, we get:
H = [(x * tan(43 degrees)) / tan(32 degrees)] * h
Therefore, the height of the tower can be found using the formula:
Height of the tower = [(x * tan(43 degrees)) / tan(32 degrees)] * h
Note: The values of 'x' and 'h' are not given in the question, so we need additional information to substitute into the formula and find the exact height of the tower.