Charlene made the sketch below in order to find the height x of a pole. She positioned a mirror on the ground so that she could see the reflection of the top of the pole. Her height, her distance from the mirror, and her line of sight to the mirror determine the smaller triangle. The pole’s height, its distance from the mirror, and the distance from the top of the pole to the mirror form a larger similar triangle. Find the height of the pole to the nearest tenth.
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Answer:
x = 22.0 ft
Step-by-step explanation:
At the mirror, the light from the top of the pole is reflected so that the angle at which it arrives and the angle at with it leaves are equal. So the two right angled triangles also have equal angles at that point on the ground. Therefore the two triangles are similar (AA rule).
Since the triangles are similar, the ratios between corresponding sides are equal:
x / 12ft = 5.5ft / 3ft
=> x = ( 12 × 5.5 / 3 ) ft
=> x = ( 4 × 5.5 ) ft
=> x = 22.0 ft
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