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Professor Plum is standing 10 feet from a streetlamp. The light from the lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 36˚. About how high is the streetlamp? A picture is not necessary to solve the problem. 

 

thank you

 Feb 25, 2021
 #1
avatar+421 
+1

Right triangle with base $10+8=18$, angle $36^{\circ}$ and we want the height, $x$.

So $\tan(36)=\frac{18}{x}\implies x=\frac{18}{\tan(36)}\approx 24.77$.

 

Note: You can derive the exact value of $\cos(36)$ with a pentagon, and then find that $\tan(36)=\sqrt{5+\sqrt{2}}$ exactly. 

 Feb 25, 2021
 #2
avatar+30898 
+1

10 + 9 = 19 ft  =  adjacent leg of right triangle  of 36 angle

 

Height =  19 tan 36o =~  13.8 ft

 Feb 25, 2021

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