# On a sunny day, a shadow with a length of l = 50 cm is formed from a gazebo with a height of h = 15.0 m.

On a sunny day, a shadow with a length of l = 50 cm is formed from a gazebo with a height of h = 15.0 m. Determine the height of the house next to it, if the length of the shadow from it l = 5.7 m

Two right-angled triangles: one with legs, the height of the gazebo and the shadow from it, the second – the height of the house and the length of the shadow from it are similar, since the angle at which the sun shines is the same. Let us find the ratio of the legs of the height of the gazebo and the length of the shadow from it, if the height is 15 m and the length of the shadow is 0.5 m:
15: 0.5 = 30.
Find the height of the house if the length of the shadow from it is 5.7 m:
5.7 * 30 = 171m.
Answer: the height of the house is 171 m.

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