The lamp of the lantern is located at a height of 15 cm from the ground and 12 m from the vertical wall.

| September 19, 2021 | education

The lamp of the lantern is located at a height of 15 cm from the ground and 12 m from the vertical wall. A bush 25 cm high is located between the wall and the lantern at a distance of 0.5 m from the lantern. What is the height of the shadow cast by the bush on the wall?

Let’s draw an additional straight line A1K1D1 parallel to AKD.

Let us prove that triangle A1CD1 is similar to triangle A1BK1.

Both triangles are straight, since CD and BK are perpendicular to AD, and the angle A is common for the triangles, then the triangles are similar in acute angle.

Segment BK1 = BK – AA1 = 0.25 – 0.15 = 0.1 m.

CD1 / BK1 = A1D1 / A1K1.

CD1 / 0.1 = 12 / 0.5.

0.5 * CD1 = 12 * 0.1.

0.5 * CD1 = 1.2.

CD1 = 1.2 / 0.5 = 2.4 m.

Then CD = CD1 + DD1 = 2.4 + 0.15 = 2.55 m.

Answer: The height of the shadow is 2.55 meters.



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