If a 48 m tall building has a shadow of `48 sqrt(3)` m , then the angle of elevation of the sun is

Options

A. `15^@`
B. `60^@`
C. `45^@`
D. `30^@`

Answer

To find the angle of elevation of the sun given a 48 m tall building and a shadow of \(48 \sqrt{3}\) m, we can follow these steps:

### Step 1: Identify the components
We have a right triangle formed by the height of the building (perpendicular), the length of the shadow (base), and the line of sight from the top of the building to the tip of the shadow (hypotenuse).

- Height of the building (perpendicular) = 48 m
- Length of the shadow (base) = \(48 \sqrt{3}\) m

### Step 2: Use the tangent function
The tangent of the angle of elevation (\(\theta\)) is given by the ratio of the opposite side (height of the building) to the adjacent side (length of the shadow):
\[ \tan \theta = \frac{\text{Height}}{\text{Shadow}} = \frac{48}{48 \sqrt{3}} \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ \tan \theta = \frac{48}{48 \sqrt{3}} = \frac{1}{\sqrt{3}} \]

### Step 4: Find the angle
We know from trigonometric values that:
\[ \tan 30^\circ = \frac{1}{\sqrt{3}} \]
Thus, we can conclude that:
\[ \theta = 30^\circ \]

### Final Answer
The angle of elevation of the sun is \(30^\circ\).

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