Tony and Manuel were trimming the branches of a tree. Tony was using an 18 ft ladder and Manuel was using a 24 ft ladder. Both ladders were leaning against the tree at a 40° angle, creating similar triangles. The bottom of the 18 ft ladder was 7 feet away from the tree, What is the distance the taller ladder is from the tree, measured in feet and inches?

Question

Armando Snow

Mathematics

14 December, 11:30

Tony and Manuel were trimming the branches of a tree. Tony was using an 18 ft ladder and Manuel was using a 24 ft ladder. Both ladders were leaning against the tree at a 40° angle, creating similar triangles. The bottom of the 18 ft ladder was 7 feet away from the tree, What is the distance the taller ladder is from the tree, measured in feet and inches?

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Answers (1)

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Moises Berger · Answer 1

9.33 feet = 111.96 inches

Step-by-step explanation:

If we have similar triangles, the rate between matching sides is the same.

So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):

18 / 7 = 24 / x

x = 7 * 24 / 18

x = 9.33 feet

To find this measure in inches, we just need to multiply by 12:

x = 9.33 * 12 = 111.96 inches