A vertical pole, 40 feet tall, casts a shadow onto the ground. If the angle of elevation from the tip of the shadow on the ground to the top of the pole is θ=67∘, use the dimensions given to find the length of the shadow, a, in feet. Do not include the units in your answer.

Considering the location of θ, the length of the opposite side is given and the length of the adjacent side needs to be found. The tangent of θ is equal to the ratio of the opposite side to the adjacent side.

tanθ=tan67∘=40a

Rearrange the equation to solve for a.

a=40tan67∘≈17.0feet

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ankitprmr2 ankitprmr2 · Answer 2 · 2021-11-26T07:49:57+01:00

The length of the shadow is 17 units.

Let us assume the distance from the lower end of the verticle pole and the shadow is x units.

Now,

vertical pole, 40 feet tall, casts a shadow onto the ground.

Therefore, the verticle pole makes an angle of 90 degrees with the surface.

Hence, the pole length is worked as perpendicular.

Thus,

tan67∘=40x

Rearrange the equation to solve for x.

x=40tan67∘≈17.0

Thus, the length of the shadow is 17 units.

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