A hiker is 400 meters away from the base of the radio tower.the angle of elevation to the top of the tower is 46°. How high is the tower?
draw a diagram and review your basic trig functions. It should be clear that the height h can be found using
h/400 = tan46°
To solve this, use tan θ = opposite / adjacent
Inputting the values that is given
tan 46° = x / 400, the x here is the height of the tower
tan 46° * 400 = x
x = 414.21 m
It will be easier to understand if you draw a triangle and solve it from there
the soh cah toa rules is also important to keep in mind
To find the height of the tower, we can use trigonometry. Let's call the height of the tower "h."
Since the angle of elevation is given, we can use the tangent function to solve for the height. The tangent of an angle is equal to the opposite side (height) divided by the adjacent side (distance from the base to the hiker).
tan(46°) = h / 400
To solve for h, we can rearrange the equation:
h = tan(46°) * 400
Now, let's calculate the height of the tower.
h ≈ tan(46°) * 400
h ≈ 0.965 * 400
h ≈ 386
Hence, the height of the tower is approximately 386 meters.
To find the height of the tower, we can use trigonometric functions. Specifically, we can use the tangent function.
The tangent of an angle is defined as 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 distance of the hiker from the base of the tower.
Let's assign variables to the known quantities:
- The distance from the hiker to the tower's base is 400 meters.
- The angle of elevation to the top of the tower is 46°.
Now, we have the angle and the adjacent side. We can use the tangent function to find the opposite side, which is the height of the tower.
The formula for finding the height is:
height = adjacent side * tan(angle)
Let's substitute the values into the formula and calculate the height:
height = 400 meters * tan(46°)
height ≈ 400 meters * 1.03553
Therefore, the height of the tower is approximately 414.212 meters.