Question

Tony and Manuel were trimming the branches of a tree. Tony was using an 8 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 24 ft ladder was 7 ft away from the tree. What is the distance (d) the taller ladder is from the tree, measured in feet and inches?

A. 20 ft 8 in
B. 20 ft 5 in
C. 20 ft 0 in
D. 20 ft 3 in

Answer 1

To find the distance the taller ladder is from the tree, use the properties of similar triangles and set up a proportion. Solve for the unknown variable to find the distance in feet and inches.

Step-by-step explanation:

To find the distance (d) the taller ladder is from the tree, we can use the properties of similar triangles. Let's label the distance from the tree to the bottom of the taller ladder as x. Since the ladders create similar triangles, we can set up the following proportion:

(x)/(8) = (7)/(24)

Cross multiplying and solving for x, we get:

x = (8 * 7) / 24 = 56 / 24 = 2.33 ft

Therefore, the distance (d) the taller ladder is from the tree is approximately 2.33 ft. Converting this to feet and inches would give us a final answer of 2 ft 4 in.