To determine the height of the pillar, a pole was used, the height of which is 2 m

| May 9, 2021 | education

To determine the height of the pillar, a pole was used, the height of which is 2 m, and the length of its shadow is 1.5 m. What is the height of the pillar if the length of its shadow is 9 m?

The pole is shown in the drawing by the segment AD, the post is BC, the length of the shade of the post is OC, the length of the shade of the pole is OD.

Triangles OBC and OAD are similar in three angles (If three angles of one triangle are equal to three corners of another triangle, then such triangles are similar). <A = <B and <D = <C – as the corresponding angles for parallel ВС and АD and secant ОВ and ОВ. If the triangles are similar, then the corresponding sides are proportional. We denote BC by x.

BC / AD = OC / OD;

BC = (AD * OC) / OD;

BC = (2 * 9) / 1.5 = 18 / 1.5 = 12 (m).

Answer. 12 meters.



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