Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second charged $45 per hour. The mechanics worke
1 answer:
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Answer: 20 ft
This problem can be solved by the Thales’s theorem, which states:
<em>Two triangles are similar when they have equal angles and proportional sides </em>
It should be noted that to apply Thales' Theorem, it is necessary to establish <u>the two triangles are similar</u>, that is, that t<u>hey have the corresponding angles equal or that their sides are proportional to each other. </u>
<u />
Now, if we measure the shadow of the flagpole and the shadow of the person, <u>at the same moment</u>, we can use the first Thales' Theorem to calculate the height of the flagpole, knowing the height of the person.
In this case we have two similar triangles (Figure attached) where is the height of the flagpole,
is the height of the person,
is the length of the shadow of the flagpole and
is the length of the shadow of the person.
Having this clear, we can write the following relation with both similar triangles:
(1)
We know all these lengths except , which is the value we want to to find.
So, in order to approach this problem we have to find from equation (1):
Then:
>>>>>This is the height of the flagpole
<u>Answer:</u>
The height of the ladder is 14.491 feet
<u>Explanation</u>:
Given the height is 11 feet
Base = 7 + 2 = 9 feet
Consider the ladder to be the hypotenuse
Applying Pythagoras Theorem,
Substituting the values in the above formula,
= 112 + 92
= 121 + 81
= 210
H = sqrt(210)
H = 14.491
Therefore, the height of the ladder is 14.491 feet