The angle of depression between a flying kite and 'a' point on the ground is 60 m. If the string makes `30^(@)`.Find the height of the kite from the ground.

Answer

To solve the problem, we need to find the height of the kite from the ground using the given information. Here’s the step-by-step solution:

### Step 1: Understand the Problem
We have a kite flying at a height above the ground. The angle of depression from the kite to a point on the ground is given, and the length of the string (which is the hypotenuse of the triangle formed) is also provided.

### Step 2: Draw a Diagram
Let’s denote:
- Point A: The point on the ground directly below the kite.
- Point B: The position of the kite.
- Point C: The point on the ground where the angle of depression is measured.

In triangle ABC:
- AB is the length of the string (hypotenuse) = 60 m.
- Angle BAC = 30° (the angle the string makes with the horizontal).
- BC is the height of the kite from the ground, which we need to find.

### Step 3: Use Trigonometric Ratios
In triangle ABC, we can use the sine function, which relates the angle to the opposite side (height of the kite) and the hypotenuse (length of the string).

The sine function is defined as:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]

For our triangle:
\[ \sin(30°) = \frac{BC}{AB} \]

### Step 4: Substitute the Known Values
We know:
- \( \sin(30°) = \frac{1}{2} \)
- \( AB = 60 \, \text{m} \)

Substituting these values into the equation gives:
\[ \frac{1}{2} = \frac{BC}{60} \]

### Step 5: Solve for BC
To find BC (the height of the kite), we can rearrange the equation:
\[ BC = 60 \times \frac{1}{2} \]
\[ BC = 30 \, \text{m} \]

### Final Answer
The height of the kite from the ground is **30 meters**.

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