A man standing x ft. from a light pole, length of man's shadow?

[Feodalherren]

Homework Statement

A man 6ft. tall is standing x ft. from a light pole 15 ft. high. Express the length of the man's shadow L as a function of x.

Homework Equations

Pre-Calc.
NO TRIG

The Attempt at a Solution

I assumed that the man's shadow creates another like triangle within in the larger one. The base of the large triangle is L + x and the height is 15 ft.
The base of the small triangle is L and the height 6 ft.

I set 15/(L+x) = (6/L) and solved for L. My solution was L(x)=(2/3)x, however, the book says it's L(x)=(3/2)x. Is it a typo or am I doing something wrong?

 

[phinds]

Homework Statement

A man 6ft. tall is standing x ft. from a light pole 15 ft. high. Express the length of the man's shadow L as a function of x.

Homework Equations

Pre-Calc.
NO TRIG

The Attempt at a Solution

I assumed that the man's shadow creates another like triangle within in the larger one. The base of the large triangle is L + x and the height is 15 ft.
The base of the small triangle is L and the height 6 ft.

I set 15/(L+x) = (6/L) and solved for L. My solution was L(x)=(2/3)x, however, the book says it's L(x)=(3/2)x. Is it a typo or am I doing something wrong?

Your process is correct and your answer is correct

 

[eumyang]

I assumed that the man's shadow creates another like triangle within in the larger one. The base of the large triangle is L + x and the height is 15 ft.
The base of the small triangle is L and the height 6 ft.

I set 15/(L+x) = (6/L) and solved for L. My solution was L(x)=(2/3)x, however, the book says it's L(x)=(3/2)x. Is it a typo or am I doing something wrong?

Looks fine to me. The book's solution is a typo.

EDIT: Oops, beaten to it by phinds.

 

[Feodalherren]

Thanks guys.