Question

The shadow of a tower standing on a level ground is found to be 40m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.

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Answer 1

$\small \mathsf{ \color{navy}{GO \: THROUGH \: THE \: ATTACHMENT}}$

Answer 2

Step-by-step explanation:

In ∆ABD,

⇒tan 60° = $\frac{AB}{BD}$

⇒√3 = $\frac{h}{x}$

∴ x = $\frac{h}{√3}$ --- eq (i)

Now,In ∆ABC,

⇒ tan 30° = $\frac{AB}{BC}$

⇒ $\frac{1}{√3}$ = $\frac{h}{x+40}$

⇒ x+40 = √3h

∴ $\frac{h}{√3}$ + 40 = 3h

⇒ h+40√3 = 3h

⇒ 2h = 40√3

⇒ h = 20√3 m

∴ The height of a tower is 20√3 m