Two ladders are leaning against a wall at the same angle as shown. how long is the short ladder? the bigger ladder has the measures of 60 and 50 ft. the smaller ladder has the measurement of 20 ft. how long is the short ladder.
Answer choices are A- 20 ft
B- 24 ft
C- 30ft
D-40ft
please help fast and thank you
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To determine the length of the shorter ladder, we need to use the concept of similar triangles.
Since both ladders are leaning against the wall at the same angle, we can create a proportion between their lengths and the lengths of their corresponding sides.
Let's set up the proportion using the given measurements:
(short ladder length) / 20ft = (big ladder length) / 60ft
We can cross-multiply and solve for the length of the shorter ladder:
(short ladder length) = (20ft * (big ladder length)) / 60ft
Given that the big ladder length is 50ft, we can substitute the value:
(short ladder length) = (20ft * 50ft) / 60ft
Now, we can calculate the length of the shorter ladder:
(short ladder length) = (1000ft) / 60ft
(short ladder length) ≈ 16.67ft
Therefore, the length of the shorter ladder is approximately 16.67 feet.