Question

Two poles AE and CD are of heights 20 m and 11m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops. ​

Answer 1

Step-by-step explanation:

(hypotenuse)2=(base)2+(perpendicular)2

Complete step-by-step answer:

Length of two poles in the problem are given as 6m and 11m and the distance between their feet is given as 12m. Hence, we need to determine the distance between their tops. Now, we can sketch the diagram with the given information as

So, here DE and AC are the poles and DC is representing the distance between their feet. As, we can observe that ∠D=∠C=∠CBE=∠BED=90∘ as AB and AC will be perpendicular to the any line joining on the ground and EB is the line parallel to the line DC (on the ground). So, all the angles mentioned above will be of 90∘ . Hence, we get sides DC and EB of equal length and ED and BC of equal length as well because BCDE will represent a rectangle if all the angles of this quadrilateral will become 90∘ . So, we get

ED = BC = 6m…………….(i)

DC = EB = 12m………….(ii)

Now, we can get the length AB of ΔABE by difference of sides AC and BC. Hence, length AB is given as

AB = AC – BC

We know AC = 11m from the problem and BC = 6m from the equation (i). So, we get

AB = 11 – 6 = 5m

AB = 5m

So, we get the sides AB and BE as 5m and 12m respectively. Now, we know the ∠CBE is 90∘ as BCDE is a rectangle. Now, we can use the property of a linear pair which is given as the angle on a point of a line is 180∘ always. Hence, the ∠CBA is 180∘ . It means the sum of ∠CBE,∠ABE is 180∘ . So, we have ∠CBE+∠ABE=180∘ as ∠CBE=90∘ so,

90+∠ABE=180∘∠ABE=180∘−90∘=90∘

Hence, ΔABE can be given as

Now, we can use Pythagoras theorem of a right angle triangle to get the side AE i.e. the distance between the tops of poles. So, Pythagoras theorem is given as

(hypotenuse)2=(base)2+(perpendicular)2

Hence, we know AE is a hypotenuse of ΔABE . So, we can get the equation as

(AE)2=(BE)2+(AB)2

Now, put AB = 5m and BE = 12m. So, we get

(AE)2=(12)2+(5)2=144+25(AE)2=169

Now, taking the square root to both sides. We get

AE=169−−−√=13m

Hence, the distance between the tops of the poles is 13m.