Question

If the altitude of the sun is at 60° then the height of the vertical tower that will cast a shadow of length 30m is

Answer 1

Answer:

30√3m

Step-by-step explanation:

angle of elevation = thetha =60°

tan 60° = height of tower / shadow length = h/30

√3 = h/30

h= 30√3m

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{Height \: of \: the \: shadow \: of \: tower = 30 \: m} \\ \sf{Angle \: of \: elevation = 60^{\circ}} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the height of the tower.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

Let height of tower be x.

We know that,

$\Large{\star{\boxed{\sf{tan \: \theta = \dfrac{Perpendicular}{Base}}}}}$

Where,

• Base = Height of shadow
• Perpendicular = Height of tower

$\rule{150}{2}$

$\sf{tan 60^{\circ} = \frac{x}{30}}$

$\Large{\star{\boxed{\sf{tan \: 60^{\circ} = \sqrt{3}}}}}$

$\sf{\mapsto x = 30\sqrt{3} \: m}$

$\therefore$ Height of tower is 30√3 m.

$\rule{200}{2}$

★ Refer the given below diagram

$\setlength{\unitlength}{1.3 pt}\begin{picture}(100,100)(0,0)\put(0,10){\line(1,0){95}}\put(40,10){\line(0,1){55}}\put(95,10){\line(-1,1){85}}\multiput(0,65)(6,0){7}{\line(1,0){3}}\put(92,11){\circle{4}}\put(10,95){\circle*{20}}\put(38,66){\circle{1.6}}\put(24,40){ \sf{x \: m} }\put(15,50){ \bf{Tower} }\put(60,0){ \sf{30\: m} }\put(20,68){ 60^{\circ} }\put(75,12){ 60^{\circ} }\put(10,105){ \bf Sun }\put(40,3){ \sf B }\put(40,68){ \sf A }\put(95,3){ \sf C }\end{picture}$