Question

Two trees are 13 m and 25 m high. If the distance between their tops is 13 m. Find the distance between their feet.

Answer 1

Given:-

Two trees of measure: 25 m and 18 m (AD & CE)

The distance between their tops is 13 m (AC)

To find:-

The distance between the foots of Tree A and Tree B (DE)

Solution:-

According to the figure (attachment), it is clear that, DE = BC and AB, BC, AC forms a right-angled triangle.

Right-angled Triangle:-

• AB = 12 cm (25-18)
• AC = 13 cm
• BC = ?

Using Pythagoras theorem, we can find the measure of BC.

${a}^{2} + {b}^{2} = {c}^{2}$

• a = Leg = AB
• b = Base = BC
• c = Hypotenuse = AC

Now substituting the measures:-

=>(AB)^2 + b^2 =(AC)^2

=> (12)^2 + b^2 = ( 13 ) ^2

=> 144 + b^2 = 169

=> b^2 = 169 - 144

=> b^2 = 25

=> b = √25

=> b = 5 m

=> BC = DE

Therefore, the distance between their foots is 5 metres.

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