Question

the angles of elevation of the top of a tower from two points at a distance of 4 metre and 9 metre from the base of the tower and in the same straight line with it are complementary prove that the height of the tower is 6 metre ​

Answer 1

$\huge{\underline{\underline{\pink{\mathfrak{AnSwEr:}}}}}$

Given :

α and β are Complimentry angles.

BC = 4 m

CD = 5 m

BD = BC + CD = 4 + 5 = 9 m

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To Prove :

Height of Tower be 6 m

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Proof :

In ΔABC

Tanα = AB/BC

Tanα = AB/4 ........(1)

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Now In Δ ABD

Tanβ = AB/BD

As α and β are Complimentry angles

⇒Tan(90° - α) = AB/9

⇒Cotα = AB/9

⇒1/Tanα = AB/9

★ Put value of Tanα

⇒1/AB/4 = AB/9

⇒4/AB = AB/9

⇒4*9 = AB*AB

⇒36 = AB²

⇒AB = √36

⇒AB = 6 m

∴ So, height is 6m

Hence Proved

Answer 2

Answer:

Step-by-step explanation: