SOLUTION: a lighthouse casts a 72- yard shadow at the same time as a 32-foot tall bill board casts a 19-foot shadow what is the height of the lighthouse

Question 314914: a lighthouse casts a 72- yard shadow at the same time as a 32-foot tall bill board casts a 19-foot shadow what is the height of the lighthouse
Found 2 solutions by rfer, solver91311:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
32/19=216/x
32x=4104
x=128.25 ft
128.25/3=42.75 yds
--------------------
32/19=72/x
32x=1368
x=42.75 yds
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the height of the lighthouse. We know from the proportionality of similar triangles that:

Cross-multiply and solve.

Notes about the precision of your answer. Since 19 will not divide evenly into 32 times 72, you are going to come out with a decimal fraction representing a number of yards of height. However, the least precise measurements in the given data is to the nearest yard. Therefore, the results of any calculations involving these data is properly expressed to the level of precision of the least precise measurement. Hence, it is correct to express your answer to this question rounded to the nearest whole yard, and it is technically incorrect to express the answer to any greater precision.

John

RELATED QUESTIONS
A 6-foot tall man casts a 10-foot shadow. At the same time and location, a tree casts a... (answered by nerdybill)
a 12 foot tree casts a 16 foot shadow. How many feet tall is a nearby tree that casts a... (answered by checkley77)
A 12-foot tree casts a 16-foot shadow. How many feet tall is a nearby tree that casts a... (answered by rfer)
A 12-foot tree casts a 16-foot shadow. How many feet tall is a nearby tree that casts a... (answered by gwendolyn)
A tree casts a shadow of 12 feet. At the same time a 6-foot man casts a 3-foot... (answered by checkley79)
A Flagpole casts a 75-foot shadow at the same time a tree 20 feet tall casts a shadow of... (answered by rfer)
A 5-foot tall woman casts a shadow of 6 feet. At the same time, a tree casts a shadow of... (answered by Boreal)
A tree cast a shadow 60 Feet long. At the same time, an 8-foot post casts a 12-foot... (answered by rfer)
A person 5 feet 3 inches tall casts a 6-foot shadow. At the same time, a lamppost casts... (answered by greenestamps)