Question

Two holes of height 25m and 5m are perpendicular to the ground.If the length of the shadow of bigger pole due to sunlight is 150m,then how long will be the shadow of the smaller pole at the same time is__________m​

Answer 1

♧Answer

12 m

♧For explain

Given length of the pole AC=8mAC=8m and formed the

shadow of length of BC=xBC=x which form a

triangle ΔABCΔABC and

The length of the pole PR=4mPR=4m and formed

the shadow of length of RQ=6mRQ=6m which form a

triangle ΔPRQΔPRQ

Now in triangle ΔABCΔABC and ΔPRQΔPRQ

Pole and shadow are perpendicular to each other

∠C=∠R=90∘∠C=∠R=90∘

As we are measuring the shadow of poles at same time so the angle of depression will be equal

∠B=∠Q∠B=∠Q

So, ΔPQR∼ΔABCΔPQR∼ΔABC by AA similarity

Now, we can say that the ratio of corresponding sides is equal

PQ/AB=QR/BC=PR/AC

PQ/AB=QR/BC=PR/AC

PR/AC=QR/BC

Now substituting the value of PR= 4m, QR= 6m, AB=8m and BC=x we get

⇒⇒ 48=6x48=6x

On solving we will get the value of xx

⇒ x=12m