A 30 metres long ladder is placed against a wall 15 m high such that it just reaches the top of the wall. The angle made by the ladder with the horizontal is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

To find the angle made by the ladder with the horizontal, we can use trigonometric ratios. Here’s how to solve the problem step by step:

### Step 1: Understand the problem
We have a right triangle formed by the wall, the ground, and the ladder. The height of the wall (opposite side) is 15 m, and the length of the ladder (hypotenuse) is 30 m.

### Step 2: Identify the trigonometric function to use
We can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, the opposite side is the height of the wall (15 m), and the hypotenuse is the length of the ladder (30 m).

### Step 3: Set up the equation
Using the sine function, we can write:
\[ \sin(\theta) = \frac{15}{30} \]

### Step 4: Simplify the ratio
\[ \sin(\theta) = \frac{1}{2} \]

### Step 5: Find the angle
Now, we need to find the angle \( \theta \) for which the sine value is \( \frac{1}{2} \). From trigonometric tables or using a calculator, we know:
\[ \theta = 30^\circ \]

### Final Answer
The angle made by the ladder with the horizontal is \( 30^\circ \).

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