7.3 Practice Problems:
Use what you know about similar triangles to discover the missing dimensions! Typical math rules apply: Don't forget the units and show your work (either in the "Show Your Work" spaces in each problem or by attaching a picture of your written work on paper at the end).
A person 5 feet 3 inches tall casts a 6-foot shadow. At the same time of day, a lamppost casts an 18-foot shadow.
What is the height of the lamppost?
A flagpole 4 meters tall casts a 6-meter shadow. At the same time of day, a nearby building casts a 24-meter shadow.
How tall is the building?
Five-foot-tall Melody casts an 84-inch shadow. At the same time of day, her friend's shadow is 1 foot shorter than her shadow.
How tall is Melody's friend? Round your answer to the nearest inch.
Juanita, who is 1.82 meters tall, wants to determine the height of a tree in her backyard. From the tree's base, she walks 12.2 meters along the tree's shadow to a position where the end of her shadow exactly overlaps the end of the tree's shadow. She is now 6.1 meters from the end of the shadows.
How tall is the tree?
At a certain time of day, a 6-foot man casts a 4-foot shadow. At the same time of day, a tree casts an 18-foot shadow.
How tall is the tree?
Private eye Samantha Diamond places a mirror on the ground between herself and an apartment building and stands so that when she looks directly into the mirror, she sees into a window. The mirror's crosshairs are 1.22 meters from her feet and 7.32 meters from the base of the building. Sam's eye is 1.82 meters above the ground.
How high is the window?
HINT: Draw out the triangles and label what you know!
Refer to the image within the "Show Your Work" space. Assume units are in inches and round to two decimals places.
How long is x ?
OPTIONAL CHALLENGE:
Sunrise Road is 42 miles long between the edge of Moon Lake and Lake Road and 15 miles long between Lake Road and Sunset Road. Lake Road is 29 miles long.
How long is Moon Lake?
IF YOU DID NOT use the "show your work" space in any of the above practice, upload a picture of your written pencil/paper work in this space here to share your thinking. If all of your work is in the sections above, feel free to ignore this question!
OPTIONAL CHALLENGE:
You need to add FIVE support beams under this ramp, in addition to the 3.6-meter beam, such that all beams are equally spaced.
Select the correct support beam lengths.
Hint: You should select a total of FIVE answers!