# At what angle does a sunbeam fall on the ground if a vertical pole 1.5 m long casts a shadow of 0.7 m?

January 31, 2021 | education

| The vertical pole, the shadow from this pole and the sunbeam form a right-angled triangle, in which the vertical pole and the shadow from it represent the legs of this triangle, and the sunbeam is the hypotenuse.

Let in rectangular △ ABC (∠C = 90 °) AC = 1.5 m and BC = 0.7 m – legs.

The tangent of an acute angle in a right-angled triangle is the ratio of the leg opposite to this angle to the leg adjacent to this angle:

tg∠B = AC / BC = 1.5 / 0.7 = 15/7 = 2.1429.

Using the Bradis tables, we find the degree measure ∠B:

∠B ≈ 65 °.

Answer: ∠B ≈ 65 °.

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