From the top of a building, the angle of depression to a point on the ground 50 m away from the base is 30°. Find the height of the building (in metres, correct to two decimal places).

From the top of a building, the angle of depression to a point on the ground 50 m away from the base is $3 0^{\circ}$ . Find the height of the building (in metres, correct to two decimal places).

easy 2 marks Class 10 · Mathematics · Introduction to Trigonometry

Answer

28.87 m

The correct answer is $28.87 m$ — Rounded to two decimal places, $h = 28.87 m$ .

Angle of depression equals the angle of elevation from the point on the ground, so $θ = 3 0^{\circ}$ .
In the right triangle formed, $tan θ = \frac{height}{horizontal distance}$ .
Thus $tan 3 0^{\circ} = \frac{h}{50}$ , where $h$ is the height.
Since $tan 3 0^{\circ} = \frac{1}{3}$ , we have $\frac{1}{3} = \frac{h}{50}$ .
Multiply both sides by 50: $h = 50 \times \frac{1}{3}$ .
Calculate $h \approx 50 \times 0.57735 = 28.8675$ .
Rounded to two decimal places, $h = 28.87 m$ .

Common mistake: Using

tan θ = \frac{adjacent}{opposite}

and getting a reciprocal value.

Concept tested: Angle of depression/elevation