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A 33-m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 34m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

Sagot :

Sqdancefanidn

Answer:

  8.2 m

Step-by-step explanation:

You want the length of the shadow whose tip is 34 m from the top of a 33 m building.

Hypotenuse

The described geometry can be modeled by a right triangle with one leg 33 m and hypotenuse 34 m. The Pythagorean theorem tells us the length of the other leg is ...

  a² +b² = c²

  b² = c² -a²

  b = √(c² -a²)

  b = √(34² -33²) ≈ 8.2 . . . . meters

The length of the shadow is about 8.2 meters.

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Additional comment

The angle of elevation to the top of the building can be found from the trig relation ...

  Sin = Opposite/Hypotenuse

And the length of the shadow can be found from the relation ...

  Cos = Adjacent/Hypotenuse

If α is the angle of elevation, then ...

   sin(α) = 33/34   ⇒   α = arcsin(33/34)

and

  Adjacent = Hypotenuse × cos(α)

  Adjacent = 34·cos(arcsin(33/34)) ≈ 8.2 . . . . meters

where the "adjacent" side of the triangle is the side between the building and the tip of the shadow, along the ground.

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