A ladder 20 m long s leaning against a vertical wall. It makes an angle of `30^(@)` with the ground. How high on the wall doe the ladder reach ?
A. 10 m
B. `17.32` m
C. `34.64` m
D. 30 m

Options

A. C
B. D
C. B
D. A

Answer

To solve the problem of how high the ladder reaches on the wall, we can use trigonometric functions. Here’s a step-by-step solution:

### Step 1: Understand the Setup
We have a right triangle formed by the ladder, the wall, and the ground. The ladder acts as the hypotenuse, the height it reaches on the wall is the opposite side, and the ground is the adjacent side.

### Step 2: Identify the Given Information
- Length of the ladder (hypotenuse, AC) = 20 m
- Angle with the ground (∠CAB) = 30 degrees

### Step 3: Use the Sine Function
To find the height (AB) that the ladder reaches on the wall, we can use the sine function:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]
Here, the opposite side is the height (AB) and the hypotenuse is the length of the ladder (AC).

### Step 4: Plug in the Values
Substituting the known values into the sine function:
\[ \sin(30^\circ) = \frac{AB}{20} \]
We know that \(\sin(30^\circ) = \frac{1}{2}\).

### Step 5: Solve for AB
Now we can set up the equation:
\[ \frac{1}{2} = \frac{AB}{20} \]
To find AB, multiply both sides by 20:
\[ AB = 20 \times \frac{1}{2} = 10 \text{ m} \]

### Conclusion
The height that the ladder reaches on the wall is **10 m**.

### Answer
A. 10 m

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