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

nicoledakota2290 Feb 25, 2021

#1**+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.**

thedudemanguyperson Feb 25, 2021

#2**+1 **

10 + 9 = 19 ft = adjacent leg of right triangle of 36 ^{o }angle

Height = 19 tan 36^{o} =~ 13.8 ft

ElectricPavlov Feb 25, 2021