At a horizontal distance of 34 meters from the base of a tower, the angle of elevation to the top is 72 degrees. Find the line of sight distance to the nearest meter.
34/d = cos 72°
now just solve for d.
To solve this problem, we can use basic trigonometry.
Let's denote the line of sight distance as "d."
Since we are given the angle of elevation, we can use the tangent function to find the value of d.
Tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the tower, and the adjacent side is the horizontal distance from the base of the tower.
Therefore, we can write:
tan(72°) = height of the tower / 34m
To solve for the height of the tower, we rearrange the equation:
height of the tower = tan(72°) * 34m
Using a scientific calculator, we can find:
height of the tower ≈ 90.139m (rounded to three decimal places)
Therefore, the line of sight distance to the nearest meter is approximately 90 meters.
To find the line of sight distance to the nearest meter, we can use trigonometry. Specifically, we can use the tangent function.
Let's label the line of sight distance as "d". From the given information, we know that the tower forms a right triangle with the horizontal distance of 34 meters and the angle of elevation of 72 degrees.
In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the tower and the adjacent side is the horizontal distance.
Using the tangent function, we have:
tan(72 degrees) = height / 34
To solve for the height, we can rearrange the equation:
height = tan(72 degrees) * 34
Calculating this equation:
height = tan(72 degrees) * 34
≈ 98.15 meters
Therefore, the line of sight distance, which is the hypotenuse of the right triangle, is the sum of the horizontal distance and the height:
d = 34 + 98.15
≈ 132.15 meters
Rounding to the nearest meter, the line of sight distance is approximately 132 meters.