Question

Two poles 18 m and 13 m high, stand upright in a playground. If their feet are 12 m apart ,find the distance between their tops.​

Answer 1

Given that:

• Two poles 18 m and 13 m high, stand upright in a playground.
• Their feet are 12 m apart.

To Find:

• The distance between their tops.

Let us assume:

• One of the pole be BD = 18 m
• Another pole be AE = 13 m
• AB be the separation between their feet = 12 m
• ED be the distance between their tops.

In rectangle ABCE:

ㅤ↠ㅤAE = BC

ㅤ↠ㅤAE = BD - CD (∵ BD = BC + CD)

ㅤ↠ㅤ13 m = 18 m - CD

ㅤ↠ㅤCD = 18 m - 13 m

ㅤ↠ㅤCD = 5 m

And,

• AB = EC = 12 m

In △ ECD:

• EC = 12 m
• CD = 5 m

By using pythagoras theorem:

ㅤ↠ㅤ(ED)² = (EC)² + (CD)²

ㅤ↠ㅤ(ED)² = (12 m)² + (5 m)²

ㅤ↠ㅤ(ED)² = 144 m² + 25 m²

ㅤ↠ㅤ(ED)² = 169 m²

ㅤ↠ㅤ(ED)² = (13 m)²

ㅤ↠ㅤED = 13 m

Hence,

• The distance between their tops is 13 m.