the angle of depression of a point sitauted at a distance of 70m from the base of the tower is 60 degree. the height of the tower is?

The problem involves finding the height of the tower using the given information: 

- The angle of depression is \(60^\circ\).
- The distance from the point to the base of the tower is 70 meters.

We can model this scenario using a right triangle, where:
- The height of the tower is the opposite side of the angle of depression.
- The distance from the point to the base of the tower is the adjacent side of the angle.
- The angle of depression is given as \(60^\circ\).

### Using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Here, \(\theta = 60^\circ\), the opposite side is the height \(h\) of the tower, and the adjacent side is 70 meters.

\[
\tan(60^\circ) = \frac{h}{70}
\]

We know that \(\tan(60^\circ) = \sqrt{3}\), so:

\[
\sqrt{3} = \frac{h}{70}
\]

Now, solve for \(h\):

\[
h = 70 \times \sqrt{3}
\]

\[
h = 70 \times 1.732 \approx 121.24 \, \text{meters}
\]

### Therefore, the height of the tower is approximately **121.24 meters**.

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the formula for calculating the height if the angle of elevation is given instead of depression?
2. How do you calculate the angle of elevation if the height and distance are known?
3. Can we apply the sine or cosine rule in this situation? Why or why not?
4. What happens if the angle of depression is less than \(60^\circ\)?
5. How does the value of the tangent function change with different angles?

### Tip:
Always ensure the angle of depression is measured from the horizontal line downwards to avoid confusion with the angle of elevation, which is measured upwards.

The angle of depression of a point situated at a distance of 70m from the base of the tower is 60 degrees. What is the height of the tower?

Learn how to calculate the height of a tower given a 60-degree angle of depression and a 70-meter distance from the base using trigonometric functions. This detailed step-by-step solution covers key trigonometric concepts and the tangent formula, suitable for Grades 9-10.

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