Determine the height of the cell tower if it casts a 118m long shadow, and at the same time, the length of the shadow

univerkov | February 9, 2021 | education

Determine the height of the cell tower if it casts a 118m long shadow, and at the same time, the length of the shadow from a one and a half meter pole stuck vertically into the ground is 2.4m.

Let us prove that the triangle AСD is similar to the triangle ABK.

Both triangles are straight, since СD and ВK are perpendicular to AD, and the angle A is common for the triangles, then the triangles AСD and AВK are similar in acute angle.

СD / ВK = AD / AK.

СD / 1.5 = 118 / 2.4.

2.4 * СD = 1.5 * 118.

2.4 * СD = 177.

AD = 177 / 2.4 = 73.75 ≈ 74 m.

Answer: The height of the cell tower is 74 meters.

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