A SPOTLIGHT ON THE GROUND SHINES ON A WALL 12 M AWAY. IF A MAN 2 M TALL WALKS FROM THE SPOTLIGHT...

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
This related rates triangle problem is a good example of a related rates calculus word problem. Even if you don't have this specific problem required for homework, this related rates triangle problem is a good demonstration of techniques that can be used in other related rates problems dealing with related rates and other geometric shapes. That's because it can be solved using the same 4 step process as all other related rates calculus word problems:
0:00 A spotlight on the ground shines on a wall 12 m away.
0:58 Draw a sketch
5:28 Come up with your equation
10:09 Implicit Differentiation
12:25 Solve For the Desired Rate of Change
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[@JakesMathLessons]

0:00 A spotlight on the ground shines on a wall 12 m away.
0:58 Draw a sketch
5:28 Come up with your equation
10:09 Implicit Differentiation
12:25 Solve For the Desired Rate of Change

[@Maya-xs9xn]

One of my favorite math tutors. Thank you.

[@JakesMathLessons]

You’re welcome, and thank you!

[@alleeyaaryannabintiabdulma6706]

thank you so much I spent 2 days trying to solve this type of problem

[@JakesMathLessons]

You’re welcome, I’m glad it helped!

[@whatisahandleeee]

Lots me a little bit towards the end because I was showed a different way, but the first half really helped me understand. I ended up just using a different equation and solving it differently, but came to the same conclusion. Thanks.

[@JakesMathLessons]

Yeah that’s the interesting thing about related rate, sometimes there’s multiple ways to do it that are all right. Good work!

[@katiebell1138]

Thanks again. Awesome job at explaining clearly.

[@JakesMathLessons]

Thank you!

[@ddahstan6876]

Awesome Jake. Very clear and helpful strategies!

[@JakesMathLessons]

Great! I’m glad it helped!

[@ac_cor_dingly]

Thank you so so much! Really really helpful!

[@JakesMathLessons]

You’re welcome! I’m glad it helped!