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A pole tilts at an angle of 9 degrees from vertical, away from the sun. The pole casts a shadow that is 24 feet long. The angle of elevation from the end of the pole’s shadow to the top of the pole is 53 degrees. How long is the pole?

Respuesta :

irspow

Answer:

Step-by-step explanation:

180-53-(90-9)=46

sin53/p=sin46/24

p=24sin53/sin46

p=26.65ft

onyebuchinnaji

The length of the pole with the given shadown is 26.6 feet long.

Length of the pole

The height of the pole is determined from trignometry property of right triangle.

The shadow of the pole, vertical height formed by the pole and the length of the pole, will form a right triangle.

  • Let the base of the right triangle = 24 ft
  • Let the base angle = 53⁰
  • base angle of similar triangle = (90 - 53) + 9 = 46⁰

The length of the pole is calculated as follows;

L/sin53 = 24/sin46

L = (24 x sin53) / (sin 46)

L = 26.6 ft

Thus, the length of the pole with the given shadown is 26.6 feet long.

Learn more about angle of elevation here: https://brainly.com/question/25748640

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