Question

A new department store opens on a hot summer day. Kathy's job is to stand outside of the main entrance and hand out a special supplement to incoming customers. The building is 30 feet tall and casts a shadow of 8 feet wide in front of the store.If Kathy is 5 ft 6in tall, how far away from the building can she stand and still be in the shade?

Answer 1

This problem can be solved by using similar triangles. First convert the units into inches. Then, draw a vertical line signifying the height of the building. Now draw a horizontal line coming from the bottom of the line to form an L shape. Connect the ends to form a right triangle. Now, draw a vertical line (can be anywhere in the triangle) from the bottom line to the hypotenuse. This represents Kathy. Now you have drawn a triangle within the big triangle, and have similar triangles, meaning that the sides are proportional to each other. This means that you can write this equation, with the distance between Kathy and the end of the shade where it touches the ground as x. Again, units are in inches.
360/96 = 66/x
x solves for 17.6 inches
Now subtract 17.6 from 96 and you get 78.4.
Cathy is 78.4 inches from the building, or 6 feet and 6.4 inches.

Answer 2

Omg thank you SO much!

Answer 3

Glad to help ;D