Question

the angle of elevation of the top of the tower from two points at distances S and T from its foot are complementary prove that height of the tower is ST
underroot

Answer 1

the answer is ✓ab
tq it was an interesting question

Answer 2

Answer: let the height of the tower= QR

Angle of elevation=

Angle RSQ= theta

Then angle QTR= 90 degree- theta

In triangle QTR,

Tan(90 degree- theta)= QR/t

That implies: cot theta= QR/t

That implies: 1/tan theta= QR/t

That implies: tan theta=t/QR----( 1 )

Then,

In in triangle QRS,

Tan theta= QR/s-----( 2 )

From ( 1 ) and ( 2 ),

t/QR= QR/s

That implies: QR^2= st

That implies: QR= root