If the angle of elevation of the top of the tower from the point of observation at a distance of 100 M from its base is 45 degrees, then what is the height of the tower?
Answered on : 2024-01-23
Answer
To find the height of the tower when the angle of elevation is 45 degrees and the distance from the point of observation to the tower's base is 100 meters, you can use trigonometry.
1. You have the angle of elevation (45 degrees) and the distance from the observer to the base of the tower (100 meters).
2. You can use the tangent function, which is defined as:
\( \tan(\theta) = \frac{\text{height of the tower}}{\text{distance to the base}} \)
3. Plug in the values:
\( \tan(45\circ) = \frac{\text{height of the tower}}{100} \)
4. Since \( \tan(45\circ) = 1 \), you can now solve for the height of the tower:
\( 1 = \frac{\text{height of the tower}}{100} \)
5. Multiply both sides by 100 to isolate the height:
\( \text{height of the tower} = 100 \) meters.
So, the height of the tower is 100 meters [1].
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