CPM Homework Help : PC Problem 10-43

Greg’s shadow is cast on a wall by a light on the ground which is $20$ meters from the wall. Greg is $180$ centimeters tall. Express the height (in meters) of his shadow, $h$ , as a function of his distance from the wall, $d$ .

Hint:

Draw and label a diagram.

Step 1:

See diagram at right.
What expression would you use for the '?' ?

Right triangle, horizontal leg labeled 20, vertical leg labeled h, vertical segment labeled 1.8, between horizontal leg & hypotenuse, divides horizontal leg into 2 sections, section between vertical segment & vertical leg labeled, d, other section labeled question mark.

Step 2:

Write a proportion using the similar triangles in the diagram.

Answer:

$\frac{1.8}{20-\textit{d}}=\frac{\textit{h}}{20}$

Now rewrite the equation in $h =$ form.