Answer:
Option a. 4 feet
Step-by-step explanation:
see the attached figure with letter to better understand the problem
we know that
A board is half way up each ladder
so
point B is the midpoint segment AC and point F is the midpoint segment AG
Than means
AB=AC/2 -----> AB=10/2=5 units
BF is parallel to segment CG ----> by Triangle midpoint segment theorem
step 1
In the right triangle ABD
Find the length side AD
Applying Pythagorean Theorem
[tex]5^2=3^2+AD^2[/tex]
solve for AD
[tex]AD=4\ ft[/tex]
step 2
Find the length of segment DE (h)
Remember that
If two triangles are similar, then the ratio of its corresponding sides is proportional
In this problem
Triangles ABD and ACE are similar by AA Similarity Theorem
so
[tex]\frac{AB}{AC}=\frac{AD}{AE}[/tex]
substitute the given values
[tex]\frac{5}{10}=\frac{4}{AE}\\\\AE=10(4)/5=8\ ft[/tex]
[tex]AE=AD+DE[/tex] ----> by segment addition postulate
substitute
[tex]8=4+DE[/tex]
solve for DE
[tex]DE=4\ ft[/tex]
therefore
The distance from the bucket to the ground is 4 feet
