A 5.4 m high tree stands 14 steps from the house on which the floodlight is installed.
| April 4, 2021 | education
A 5.4 m high tree stands 14 steps from the house on which the floodlight is installed. The tree shadow is three steps. What is the height of the house in meters?
Determine the distance from the house to the edge of the tree shadow.
AC = AH + CH = 14 + 3 = 17 steps.
Triangles ABC and DHC are similar in acute angle, since the angle C is common for the triangles.
Their similarities are triangles: AC / AB = CH / DH.
AB = AC * DH / CH.
AB = 17 * 5.4 / 3 = 30.6 m.
Answer: The height of the house is 30.6 meters.
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