A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of elevation of the top of the building from his eye is `60^(@)`. Calculate the height of the building. (Take `sqrt3` = 1.73)

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We have a boy who is 1.7 m tall standing 50 m away from a building. The angle of elevation from the boy's eyes to the top of the building is 60 degrees. We need to find the height of the building.

### Step 2: Set Up the Diagram
Let's denote:
- The height of the building as \( h \).
- The height of the boy as \( 1.7 \) m.
- The distance from the boy to the building as \( 50 \) m.
- The angle of elevation as \( 60^\circ \).

### Step 3: Determine the Height Above the Boy's Eyes
The height of the building above the boy's eyes can be represented as \( h - 1.7 \) m.

### Step 4: Use Trigonometry
Using the tangent function, which relates the angle of elevation to the opposite side (height above the boy's eyes) and the adjacent side (distance to the building):

\[ \tan(60^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h - 1.7}{50} \]

### Step 5: Substitute the Value of \( \tan(60^\circ) \)
We know that \( \tan(60^\circ) = \sqrt{3} \approx 1.73 \). Therefore, we can write:

\[ \sqrt{3} = \frac{h - 1.7}{50} \]

### Step 6: Solve for \( h - 1.7 \)
Multiplying both sides by 50 gives:

\[ 50\sqrt{3} = h - 1.7 \]

### Step 7: Calculate \( 50\sqrt{3} \)
Substituting \( \sqrt{3} \) with \( 1.73 \):

\[ 50 \times 1.73 = 86.5 \]

### Step 8: Solve for \( h \)
Now we can substitute back to find \( h \):

\[ h - 1.7 = 86.5 \]

Adding \( 1.7 \) to both sides:

\[ h = 86.5 + 1.7 = 88.2 \text{ m} \]

### Final Answer
The height of the building is \( 88.2 \) m.

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