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 degrees . How high is the tower?
Since the hiker is 400m away from the radio tower .i.e it is at the foot .therefore we must find the height .using tan 46.
Tan 46-_opposite divided by adjacent h/400then we cross multiply then we say h_-1.036times 400then our answer is 414.4
421.21
tan 46 = h/400
414.2
To find the height of the tower, we can use trigonometry. In this case, we need to use the tangent function because we know the opposite (height) and the adjacent (distance from the base of the tower).
1. Recall that the tangent of an angle is equal to the ratio of the opposite side over the adjacent side.
So, tan(angle) = opposite/adjacent.
2. Substitute the known values into the equation:
tan(46 degrees) = height/400 meters.
3. Now we can solve for the height of the tower.
Multiply both sides of the equation by 400 meters:
400 meters * tan(46 degrees) = height.
4. Use a calculator to find the tangent of 46 degrees:
tan(46 degrees) ≈ 1.03553.
5. Multiply 400 meters by 1.03553 to find the height of the tower:
height ≈ 414.2112 meters.
So, the height of the tower is approximately 414.2112 meters.