gabrielaceleste04
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Please someone help!!!!
Kristine observes the top of a lookout tower from a point 220 ft from its base.

If the indicated angle of elevation measures 37º, how tall is the tower? Give your answer to the nearest tenth of a foot.

Please someone help Kristine observes the top of a lookout tower from a point 220 ft from its base If the indicated angle of elevation measures 37º how tall is class=

Respuesta :

semsee45

Answer:

165.8 ft (nearest tenth)

Step-by-step explanation:

We can use the tan trig ratio to calculate the height of the tower.

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

where:

  • [tex]\theta[/tex] = the angle
  • O = the side opposite the angle
  • A = the side adjacent the angle

From inspection of the diagram:

  • [tex]\theta[/tex] = 37°
  • O = height of tower (let's call this h)
  • A = 220 ft

Substituting these values into the trig tan ratio:

[tex]\sf \implies tan(37)=\dfrac{h}{220}[/tex]

Multiply both sides by 220:

[tex]\sf \implies 220tan(37)=h[/tex]

[tex]\sf \implies h=220tan(37)[/tex]

[tex]\sf \implies h=165.781891[/tex]

Therefore, the height of the tower is 165.8 ft (nearest tenth)

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