two points A and Bare 80 feetapart on the same side of A towerand on a horizontal line through its foot.if angle of elevation of the top of the tower at A is 21 degree and B is 46 degree find the height of the tower.
47.91
To find the height of the tower, we can use the concept of trigonometry and the given angles of elevation.
Let's refer to the distance from point A to the top of the tower as h (the height of the tower). We can create a right-angled triangle with the tower as the height, the distance from point A to the tower as the base, and the line connecting point A to the top of the tower as the hypotenuse.
Since we have the angle of elevation at point A as 21 degrees, we can use the tangent function to find the height. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, tan(21 degrees) = h / 80 feet.
To find h (the height of the tower), we can rearrange the equation:
h = 80 feet * tan(21 degrees).
Now, let's calculate the value:
h = 80 feet * tan(21 degrees)
h ≈ 35.94 feet.
Hence, the height of the tower is approximately 35.94 feet.
If B is at distance x from the tower of height h,
h/x = tan 46°
h/(x+80) = tan21°
so, eliminating x, we get
h/tan46° = h/tan21° - 80
Now just solve for h