I need help with this question below

Question

A pole that is 3.5m tall casts a shadow that is 1.14m long. At the same time, a nearby building casts a shadow that is 50.25m long. How tall is the building? Round your answer to the nearest meter.

Answer 1

This is where you could draw two similar triangles in which the two corresponding heights are opposite sides and the shadow lengths are adjacent sides. Ratios can be utilized to solve this problem.

 

h=height of building

 

h/3.5=50.25/1.14 Hence, h=(50.25/1.14)*3.5=154 m

Answer 2

The answer is about 154m. You can set this problem up using proportions... you have one fraction with 3.5m in the numerator and 1.14m in the denominator. Next, set that equal to another fraction with X in the numerator and 50.25m in the denominator. After that, you can cross multiply to have (3.5m)(50.25m)=(1.14m)(X) --> 175.875=1.14X --> divide both sides by 1.14 and X = 154.276316 --> you are asked to find it to the nearest meter, therefore, X = 154m

Answer 3

This is a simple proportions problem. Make sure to set it up correctly, with the dimensions of the pole and the building on two different sides, and that the shadows' lengths and the objects' heights are only in the numerator or denominator, like this:

 

 3.5  =    x   

1.14    50.25

 

Then cross multiply:

 

1.14x = (3.5)(50.25)

 

And solve for x:

 

1.14x = 175.875

x = 154.3

x = 154 meters (rounded)