Question

lamp post 5 root 3 m high casts a shadow 5m long on the ground. The sun is elevation at this
moment is ______

Answer 1

★Figure refer to attachment

Given

• Height of lamp post = 5√3m
• Length of shadow on the ground= 5m

Find out

• Sun angle elevation

Solution

★Let the elevation angle be θ

In ∆ABC

$\implies\sf tan\:\theta=\dfrac{AB}{BC} \\ \\ \\ \implies\sf tan\:\theta=\dfrac{5\sqrt{3}}{5} \\ \\ \\ \implies\sf tan\:\theta=\sqrt{3} \\ \\ \\ \implies\sf tan\:\theta=tan\:60\degree\:\:\:\:\red{[tan\:60\degree=\sqrt{3}]} \\ \\ \\ \implies\sf \theta=60\degree$

Hence,

• Elevation angle = 60°

Additional Information

• sin θ = perpendicular/hypotenuse

• cos θ = perpendicular/base

• tan θ = perpendicular/base

Answer 2

Given :

• Height of the lamp post = $\sf 5\sqrt{3} m$

• Length of the shadow on the ground = 5m

To Find :

• The sun is elevation at this moment = ?

Figure :

$\setlength{\unitlength}{1.6cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{C}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(8.9,0.7){\sf{\large{5m}}}\put(6.8,2){\sf{\large{5 root 3 m}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\qbezier(9.8,1)(9.7,1.25)(10,1.4)\put(9.6,1.2){\sf\large{\theta }}\end{picture}$

Solution :

Let the angle of elevation be $\sf theta$

In ∆ABC,

$\dashrightarrow\:$ $\sf tan\: \theta = \dfrac{AB}{BC}$

$\dashrightarrow\:$ $\sf tan\: \theta = \dfrac{5\sqrt{3}}{5}$

$\dashrightarrow\:$ $\sf tan\: \theta = \sqrt{3}$

$\gray\dashrightarrow\:$ $\underline{\boxed{\gray{ \sf \theta = 60^{\circ}} }}$ $\red\bigstar$

Therefore, The sun is elevation at this moment is 60°

$\underline{\rule{210}3}$

Extra brainly knowledge :

$\boxed{\begin{minipage}{20 em} \sf \displaystyle \bullet sin \theta = \dfrac{perpendicular}{hypotenuse} \\\\\\ \bullet </p><p>cos \theta = \dfrac{perpendicular}{base} \\\\\\ \bullet tan \theta = \dfrac{perpendicular}{base}\right) \end{minipage}}$

$\underline{\rule{210}3}$