The angle of elevation of the top of a tower 40 m high is 37° when seen from a point on the ground level. What is the distance of a point from the foot of the tower?
as before,
40/x = tan37°
To find the distance of a point from the foot of the tower, we can use trigonometry and the given angle of elevation.
Let's denote the distance from the point on the ground level to the foot of the tower as "x".
We can form a right triangle with the tower height (40 m), the distance from the foot of the tower (x), and the line of sight from the point on the ground level to the top of the tower.
In a right triangle, the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.
In this case, the tangent of the angle of elevation (37°) is equal to the height of the tower (40 m) divided by the distance from the foot of the tower (x).
So we have: tan(37°) = 40/x.
To find the value of x, we can rearrange the equation as x = 40 / tan(37°).
Now, let's calculate the value of x:
x ≈ 40 / tan(37°) ≈ 40 / 0.7536 ≈ 53.1464 m.
Therefore, the distance from the point to the foot of the tower is approximately 53.1464 meters.
To find the distance from the foot of the tower to the point, we can use trigonometry.
Let's assume the distance from the point to the foot of the tower is 'x'.
We have the height of the tower (opposite side) as 40 m and the angle of elevation (angle between the ground and line of sight to the top of the tower) as 37°.
Using trigonometry, we can use the tangent function to solve for 'x'.
Tangent(37°) = Opposite / Adjacent
Tan(37°) = 40 / x
Rearranging the equation, we have:
x = 40 / Tan(37°)
Now we can calculate the value of 'x'.
x ≈ 40 / 0.7536
x ≈ 53.1 meters
Therefore, the distance of the point from the foot of the tower is approximately 53.1 meters.