Answer:
a) ΔCED ~ ΔCAB
b) 157.5 m
Explanation:
The similarity statement for geometric figures lists the corresponding vertices in the same order. Corresponding sides of similar figures are proportional. That fact can be used to find the missing side length.
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a)
The right angles are corresponding. Angle C corresponds to itself, so the similarity statement can be written ...
ΔCED ~ ΔCAB
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b)
Corresponding sides are proportional, so we can write ...
AB/AC = ED/EC
AB/(50+160) = 120/160 . . . . . using the numerical values
AB = 210 × 120/160 = 157.5 . . . meters
The length of the lake is 157.5 meters.