the angle of elevation to the tower is 30 degree and then moved towards the tower of a distance 20m.now thw angle of elevation is 60 degree.What is the height of the tower??plz help me:)
Assume you start a distance x from the tower of height y.
y = x tan(30°)
y = (x-20) tan(60°)
Solve for y.
4.9m
To find the height of the tower, we can use simple trigonometry based on the given information. Let's break down the steps:
Step 1: Set up a triangle representing the situation described:
- The tower represents the vertical side (height) of the triangle.
- The distance moved towards the tower (20m) represents the horizontal side (base) of the triangle.
- The angle of elevation at the starting point (30 degrees) and the new position (60 degrees) represent the angles in the triangle.
Step 2: Determine the height of the tower using the tangent function:
- Recall that tan(x) = opposite/adjacent.
- In this case, the opposite side is the height of the tower (h) and the adjacent side is the distance moved towards the tower (20m).
At the starting point:
tan(30) = h/20
h = 20 * tan(30)
At the new position:
tan(60) = h/(20+20)
h = 40 * tan(60)
Step 3: Simplify the equations and solve for h:
h = 20 * √3 (approx. 34.64)
h = 40 * √3 (approx. 69.28)
Therefore, the height of the tower is approximately 34.64 meters at the starting point and approximately 69.28 meters at the new position.