The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st. -Maths 9th

The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st. -Maths 9th
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1 Answer

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
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