Solve each problem. See Example 5.
Height of a Lighthouse The B...

Question

Solve each problem. See Example 5. 
 Height of a Lighthouse The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 A.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?

Accepted Answer

Hello, everyone. We are told that at any instance, the shadow of pole A is 80 m long while the shadow of pole B is 60 m long, we want to find the height of pole B. If the height of pole A is 15 m, our answer choices are A 30 m B 7.5 m C 60 m D 100 m. There's a couple ways you can do this. I'm gonna draw a small picture. So I'm gonna start by drawing, pull A, we know that it is 15 m tall and we know it has a shadow of 80 m and I'm going to just make a dotted line to close off the triangle. Then for Pole B, we know nothing about its height. That's what we're trying to find out. So I'm gonna call that X and we know its shadow is 160 m long. And again, I'm gonna just close off my triangle with a dotted line. Since this is happening at the same time, we can say these are similar triangles and we can set up a proportion to solve them. There's a couple different ways you can set up that proportion. What I'm gonna do is the height of the pole divided by the shadow of Paul A equals the height of the pole divided by the length of the shadow of pole B. So I have 15, divided by 80 equals X divided by 160. Now I'm going to cross multiply 80. Multiplied by X is 80 X 15, multiplied by 160 is 2400. Solving for X I divide both sides by and we get the X equals 30. So we're looking for a length here. So we know it's in meters. So this would be 30 m. So that is the height of pole B and it's answer choice. A 30 m have a nice day.

Solve each problem. See Example 5. Height of a Lighthouse The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 A.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?

Key Concepts

Similar Triangles

Proportional Relationships

Trigonometric Ratios

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