The respective ratio between the height of tower and the point at some distance from its foot is `5sqrt(3):5` .What will be the angle of elevation of the top of the tower ?

Options

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

Answer

To solve the problem step by step, we will use the information given about the height of the tower and the distance from its foot.

### Step 1: Understand the Ratio
The problem states that the ratio between the height of the tower and the distance from its foot is given as \(5\sqrt{3} : 5\). This means:
- Height of the tower (h) = \(5\sqrt{3}\)
- Distance from the foot of the tower (d) = \(5\)

### Step 2: Set Up the Trigonometric Relationship
We need to find the angle of elevation (θ) of the top of the tower from the point at distance d. The relationship between the height (h), distance (d), and angle (θ) can be expressed using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{d} \]

### Step 3: Substitute the Values
Substituting the values of h and d into the equation:
\[ \tan(\theta) = \frac{5\sqrt{3}}{5} \]

### Step 4: Simplify the Expression
Now, simplify the right-hand side:
\[ \tan(\theta) = \sqrt{3} \]

### Step 5: Find the Angle θ
We know from trigonometric values that:
\[ \tan(60^\circ) = \sqrt{3} \]
Thus, we can conclude:
\[ \theta = 60^\circ \]

### Conclusion
The angle of elevation of the top of the tower is \(60^\circ\).

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