Question

Jim is 4 ft from a lamppost that is 16 ft tall and he is 6 foot tall his shadow is ____?____ ft long?

Answer 1

 

To solve this, let us first imagine a smaller triangle created by the head of Jim (A), the top of the lamp post (B), and somewhere on the body of the lamp post which is directly perpendicular to the head of Jim (C).

 

CB = 16 – 6 = 10 ft

AC = 4 ft

 

Calculate for angle B using tan function:

tan B = AC / CB

B = tan^-1 (4 / 10)

B = 21.8°

 

Now imagine a bigger triangle created by the tip of shadow (D), the top of the lamp post (B), and the base of the lamp post (E).

BE = 16 ft

B = 21.8°

 

We can calculate for DE using tan function:

tan B = DE / BE

(16 ft) tan 21.8 = DE

DE = 6.4 ft

 

Since Jim is 4ft away from the base of the lamp post, therefore the length of the shadow is:

6.4 ft – 4 ft

= 2.4 ft

 

Therefore the length of Jim’s shadow is 2.4 ft long