A lamp is placed at the top of a pole. When a man of height $1.5 m$ stands $12 m$ away from the pole, the angle of elevation of the lamp from the man's eyes is $2 5^{\circ}$ . Find the height of the pole. (Take the man's eye level at $1.5 m$ above the ground.)

medium MCQ 2 marks Class 10 · Mathematics · Some Applications of Trigonometry

Answer

7.1 m (approximately)

The correct answer is 7.1 m (approximately) — Round to one decimal place: $h \approx 7.1 m$ .

Step-by-step solution

Draw a right triangle with horizontal side $12 m$ and vertical side equal to the difference between the pole height $h$ and the man's eye level $1.5 m$ .
Apply the definition of tangent: $tan 2 5^{\circ} = \frac{h - 1.5}{12}$ .
Solve for $h$ : $h - 1.5 = 12 tan 2 5^{\circ}$ , therefore $h = 12 tan 2 5^{\circ} + 1.5$ .
Use $tan 2 5^{\circ} \approx 0.4663$ to get $h \approx 12 \times 0.4663 + 1.5 = 7.0956 m$ .
Round to one decimal place: $h \approx 7.1 m$ .

Common mistake: Using the man's total height instead of his eye level, or forgetting to add the

1.5 m

after computing the vertical rise.

Concept tested: Height of pole using angle of elevation