There is a lightning rod on top of a building. From a location 500 feet from the base of the building, the angle of elevation to

Question

3 years ago

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There is a lightning rod on top of a building. From a location 500 feet from the base of the building, the angle of elevation to

the top of the building Is measured to be 36 degrees. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38 degrees. Find the height of the lightning rod. Round to the nearest foot.

Mathematics

1 answer:

Kitty [74] · Answer 1 · 2022-02-26T06:15:24+03:00

<h2>Hello!</h2>

The answer is:

The height of the lightning rod is 27.4 feet.

To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.

So, writing the equations we have:

We know that the angle of elevation from the base of the buildings is 36°

Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.

Using the information we have:

To the top of the building:

$tan(\alpha )=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}$

To the top of the lightning rod:

$tan(\alpha )=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}$

Now, isolating we have:

$tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\DistanceToTheTopOfTheBuilding=tan(36\°)*BuildingBase \\\\DistanceToTheTopOfTheBuilding=tan(36\°)*500feet=363.27feet$

Also, we have that:

$tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*BuildingBase\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*500feet=390.64feet$