Question

Choose the correct answer of the following question:

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is

(a) 0° (b) 30° (c) 45° (d) 60° [CBSE 2014]

Answer 1

Let AB represents the vertical pole and BC represents the shadow on the ground and θ represents angle of elevation the sun.

$$\begin{gathered} \mathrm{In}∆\mathrm{ABC}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{x}{x}\left(\mathrm{As},\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{pole},\mathrm{AB}=\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{shadow},\mathrm{BC}=x\right) \\ \Rightarrow \tan \theta =1 \\ \Rightarrow \tan \theta =\tan 45° \\ \therefore \theta =45° \end{gathered}$$

Hence, the correct answer is option (c).