The string of a kite is 150 m long and it makes an angle `60^(@)` with the horizontal. Find the height of the kite above the ground. (Assume string to be tight)

Answer

To find the height of the kite above the ground, we can use trigonometric ratios. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a kite flying at the end of a string that is 150 meters long, making an angle of 60 degrees with the horizontal. We need to find the height of the kite above the ground.

### Step 2: Draw a Diagram
Draw a right triangle where:
- The horizontal line represents the ground.
- The hypotenuse (the string) is 150 m long.
- The angle between the string and the horizontal ground is 60 degrees.
- The vertical line represents the height (h) of the kite above the ground.

### Step 3: Identify the Triangle
In the right triangle formed:
- The hypotenuse (AC) is the length of the string = 150 m.
- The angle (C) is 60 degrees.
- The height (AB) is what we need to find.

### Step 4: Use the Sine Function
We can use the sine function, which relates the angle to the opposite side (height) and the hypotenuse:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
For our triangle:
\[ \sin(60^\circ) = \frac{h}{150} \]

### Step 5: Substitute the Value of Sine
The value of \(\sin(60^\circ)\) is \(\frac{\sqrt{3}}{2}\). Therefore, we can write:
\[ \frac{\sqrt{3}}{2} = \frac{h}{150} \]

### Step 6: Solve for h
Now, we can solve for h:
\[ h = 150 \times \frac{\sqrt{3}}{2} \]
\[ h = 75\sqrt{3} \text{ meters} \]

### Final Answer
The height of the kite above the ground is \(75\sqrt{3}\) meters.

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