Question

a tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 60 degrees. how tall is the tower

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\underline{\underline{\Huge{\textbf{Solution:}}}}$


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$\textsf{Given,}$

Length of the Shadow = 60 ft

Angle of elevation of the sun on the tower = $60^{\circ}$

Height of the tower = ? (in ft)



Let AB be the height of the tower

BC be the length of the Shadow

Now, we have a Right $\rm{\triangle{ABC}}$

We have Adjacent and Angle in the Right triangle. To find the Opposite we can Apply tan of Angle.

$\LARGE{\mathbf{In\: \triangle{ABC}}}$


$\LARGE{\boxed{\quad{\bigstar\; \; \tan\: \theta= \mathsf{\dfrac{Opposite\: (AB)}{Adjacent\: (BC)}}\quad}}}$


Substitute values

$\tan\: 60^{\circ}= \dfrac{h}{60}$

$\sqrt{3} = \dfrac{h}{60}$

$h = \rm{60\: \sqrt{3}\: ft}$


$\therefore$

$\blacksquare\; \; \textsf{The\: height\: of\: the\: tower is \:} \Large{\underline{\mathbf{60 \: \sqrt{3}\: ft}}}$