question_answer

The shadow of a tower is 15 m when the sun's elevation is \[30{}^\circ .\] What is the length of the shadow when the sun's elevation is\[60{}^\circ ?\]

A) 3 m

B) 4 m

C) 5 m

D) 6 m

Correct Answer: C

Solution :

[c] Let the required length of shadow is x m. In \[\Delta \Alpha \Beta C,\]\[\tan 60{}^\circ =\frac{AB}{BC}\]             \[\Rightarrow \]   \[AB=x\sqrt{3}\]                        (i) In \[\Delta \Alpha BD,\]\[\tan 30{}^\circ =\frac{AB}{15}\] \[\Rightarrow \]   \[\frac{1}{\sqrt{3}}=\frac{AB}{15}\] \[\therefore \]      \[AB=\frac{15}{\sqrt{3}}\]                     (ii) From Eqs. (i) and (ii), we get \[x\sqrt{3}=\frac{15}{\sqrt{3}}\] \[\Rightarrow \]   \[x=5\,m\]