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An observer (O) is located 900 feet from a building (B). The observer notices a helicopter (H) flying at a 49° angle of elevation from his line of sight. How high is the helicopter flying over the building? You must show all work and calculations to receive full credit.

An observer O is located 900 feet from a building B The observer notices a helicopter H flying at a 49 angle of elevation from his line of sight How high is the class=

Respuesta :

jensbo77

Answer: 1,035

Step-by-step explanation:

According to the meaning of the title

Let the height be x

x= 900 tan 49° ~1035 feet

(value of tangent trigonometric function for an angle)

semsee45

Answer:

1035.3 ft (nearest tenth)

Step-by-step explanation:

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • θ is the angle.
  • O is the side opposite the angle.
  • A is the side adjacent the angle.

From inspection of the given right triangle:

  • θ = 49°
  • O = h
  • A = 900 ft

Substitute the given values into the tan trig ratio and solve for h:

[tex]\implies \tan(49^{\circ})=\dfrac{h}{900}[/tex]

[tex]\implies h=900\tan(49^{\circ})[/tex]

[tex]\implies h=1035.33156...[/tex]

Therefore, the helicopter is flying 1035.3 ft (nearest tenth) over the building.

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