question_answer

Solve :

(i) A tower is 50 m high. Its shadow is x m shorter when the Sun's altitude is \[{{45}^{o}}\]than when it is \[{{30}^{o}},\] then x = ___.

(ii)The angle of elevation of the top of a tower from a point 100 m from the tower is \[{{45}^{o}}\] then the height of the tower is __.

A)

	(i)	(ii)
	\[\begin{array}{*{35}{l}}    38.6\,m~  \\ \end{array}\]	102m

               

B)

	(i)	(ii)
	\[36.6\,m\]	100m

               

C)

	(i)	(ii)
	\[36.1\text{ }m\]	98m

               

D)

	(i)	(ii)
	\[39.6\,m\]	101m

Correct Answer: B

Solution :

          (i) In \[\Delta ABC,\frac{AB}{BC}=\tan {{45}^{o}}\Rightarrow \frac{50}{BC}=1\] \[\therefore \]   \[BC=50m\] Similarly,                                                              in  \[\Delta ABD,\,\,\frac{AB}{BD}=\tan {{30}^{o}}\] \[\Rightarrow \]            \[\frac{50}{BC+CD}=\frac{1}{\sqrt{3}}\] \[\Rightarrow \]            \[50+x=50\,\sqrt{3}\] \[\Rightarrow \] \[x=50\sqrt{3}-50\] \[\Rightarrow \] \[x=36.6m\] (ii) In \[\Delta ABC,\] \[\frac{AB}{BC}=\tan {{45}^{o}}\] \[\Rightarrow \]  \[\frac{AB}{100}=1\Rightarrow AB=100m\] \[\therefore \] Height of tower is 100 m.