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A radio tower is located 325 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 43°, and that the angle of depression to the bottom of the tower is 31°. how tall is the tower?

Respuesta :

nobillionaireNobley

The height of the tower is given by [tex] 325(\tan{43^o}+\tan{31^o})=325(0.9325+0.6009)\\ \\=325(1.5334)=498.355 [/tex]

The height of the tower is 498.355 feet and this can be determined by using the trigonometric function and given data.

Given :

  • A radio tower is located 325 feet from a building.
  • From a window in the building, a person determines that the angle of elevation to the top of the tower is 43°, and that the angle of depression to the bottom of the tower is 31°.

The following steps can be used in order to determine the height of the tower:

Step 1 - According to the given data, the radio tower is located 325 feet from a building.

Step 2 - Also it is given that the angle of elevation is 43 degrees and the angle of depression is 31 degrees.

Step 3 - So, by using the data given in the above steps, the height of the tower is given by:

[tex]\rm Height = 325(tan43^\circ+tan 31^\circ)[/tex]

Step 4 - Simplify the above expression.

[tex]\rm Height = 325(0.9325+0.6009)[/tex]

Height = 498.355 feet

So, the height of the tower is 498.355 feet.

For more information, refer to the link given below:

https://brainly.com/question/21286835